Bibliography and Paper Map

Reading guide for the generalized-symmetries course. This maps each reference to its role; it is not a complete bibliography of a field that would need several hundred entries. Every entry was verified against INSPIRE-HEP, arXiv or Crossref on 2026-09-27 (78 references; record in reviews/2026-09-27-comprehensive-review.md §6); new entries are verified when they are added.

How to read the references

Three levels, same discipline as the AQFT course:

The classic spine. Semester I primary material. These get read in full, and their central calculations get reproduced in problem sets. Most are short; the style is terse and the lecture notes supply the missing steps.

Books and reviews. Companions, not spines. Students keep two open per semester (Kogut + Savit in Sem I; McGreevy + Shao in Sem II) and consult the rest.

Research papers. Semester II seminar material. For each one, the presenter must identify: the technical claim, what it needs from Semester I, the one calculation worth reproducing, and the open problem it leaves.

The classic spine (Semester I)

Reference	Course use	What to take from it
Kramers & Wannier, Phys. Rev. 60 (1941) 252	Wk 4	Order–disorder duality and T_c from self-duality; the oldest ancestor of every duality in the course.
Berezinskii, Sov. Phys. JETP 32 (1971) 493; Kosterlitz & Thouless, J. Phys. C 6 (1973) 1181	Wks 1, 4	Vortex unbinding; the energy–entropy argument in its original habitat.
Kadanoff & Ceva, Phys. Rev. B 3 (1971) 3918	Wk 4	Disorder variables μ and the order–disorder algebra; the seed of duality defects (Sem II Wk 13).
Wegner, J. Math. Phys. 12 (1971) 2259	Wk 5	ℤ₂ gauge theory; a phase transition with no local order parameter; Wilson loops before Wilson.
Wilson, Phys. Rev. D 10 (1974) 2445	Wk 6	Plaquette action, strong-coupling area law, confinement as a lattice statement.
Kogut & Susskind, Phys. Rev. D 11 (1975) 395	Wk 7	Hamiltonian lattice gauge theory; Gauss law; electric strings.
Villain, J. Physique 36 (1975) 581	Wks 3, 9	The periodic Gaussian action — the form in which every duality of the course is exact.
Elitzur, Phys. Rev. D 12 (1975) 3978	Wk 5	Local symmetries do not break; the theorem that forces loop diagnostics.
José, Kadanoff, Kirkpatrick, Nelson, Phys. Rev. B 16 (1977) 1217	Wk 3; Sem II Wk 12	The complete spin-wave ⊗ Coulomb-gas decomposition of the XY model.
Polyakov, Phys. Lett. B 59 (1975) 82; Nucl. Phys. B 120 (1977) 429	Wks 9–10	Monopole plasma, mass gap, permanent confinement in compact QED₃ — the semester’s central calculation.
Banks, Myerson, Kogut, Nucl. Phys. B 129 (1977) 493	Wks 8, 11; Sem II Wk 12	Exact duality of 4d Villain U(1); monopole Coulomb gas in 4d.
Guth, Phys. Rev. D 21 (1980) 2291	Wk 11 (statement)	The Coulomb phase of 4d compact U(1) exists — the transition is real.
Nambu, Phys. Rev. D 10 (1974) 4262; Mandelstam, Phys. Rept. 23 (1976) 245	Wk 11	The dual-superconductor picture of confinement — see dual-superconductor.
‘t Hooft, Nucl. Phys. B 138 (1978) 1	Wks 11, 14	Disorder loops, electric/magnetic flux classification; the operator language Sem II makes systematic.
Fradkin & Susskind, Phys. Rev. D 17 (1978) 2637	Wks 4, 7	Order and disorder in gauge systems; Hamiltonian dualities.
Fradkin & Shenker, Phys. Rev. D 19 (1979) 3682–3697	Wks 13–14	Gauge–Higgs phase diagrams; Higgs–confinement complementarity; what dynamical matter does to every diagnostic.
Cardy & Rabinovici, Nucl. Phys. B 205 (1982) 1	Wk 12	Oblique confinement and the SL(2,ℤ) structure of θ-vacua.
Creutz, Phys. Rev. D 21 (1980) 2308	Wk 6 (mention)	Monte Carlo enters; where the analytic expansions hand off to the machine.

Books and reviews (both semesters)

Reference	Course use	Reading strategy
Kogut, Rev. Mod. Phys. 51 (1979) 659	Sem I companion	The single best pedagogical source for Blocks A–C; read alongside every week.
Savit, Rev. Mod. Phys. 52 (1980) 453	Sem I companion; Sem II Wk 14 §6 (finite abelian dualities)	Duality systematics; the tables of “theory ↔ dual theory” students should be able to re-derive.
Polyakov, Gauge Fields and Strings (1987), ch. 4	Sem I Block C	The confinement chapters, in Polyakov’s own voice.
Fradkin, Field Theories of Condensed Matter Physics, 2nd ed. (2013)	Both semesters	The condensed-matter reading of gauge theories, disorder operators, and topological phases.
Tong, Lectures on Gauge Theory; Lectures on Statistical Field Theory	Sem I companion	When the originals are terse; the lattice and BKT chapters.
Wen, Quantum Field Theory of Many-Body Systems (2004)	Sem II Block 3	Topological order from its inventor; string condensation.
Zeng, Chen, Zhou, Wen, Quantum Information Meets Quantum Matter (2019)	Sem II Blocks 3	The quantum-information bridge, at textbook pace.
Preskill, Lecture Notes, ch. 9	Sem II Blocks 3	Topological quantum computation; the QEC reading of anyons.
Nakahara, Geometry, Topology and Physics, 2nd ed.	Sem I Wk 2 backup	Homology/cohomology chapters for students who want the continuum story.
McGreevy, arXiv:2204.03045	Sem II companion	Generalized symmetries for condensed matter; the review to keep open all semester.
Shao, “What’s done cannot be undone” (TASI), arXiv:2308.00747	Sem II companion	Non-invertible symmetries systematically; Blocks 4–5 follow its ordering.
Córdova, Dumitrescu, Intriligator, Shao (Snowmass), arXiv:2205.09545	Sem II orientation	The field map; where each seminar paper sits.
Schäfer-Nameki, arXiv:2305.18296; Bhardwaj et al., arXiv:2307.07547; Brennan & Hong, arXiv:2306.00912	Sem II alternates	Three more lecture-note routes through the same material; different students click with different ones.

Generalized symmetries and anomalies (Semester II Blocks 1–2 spine)

Reference	Course use	Required sections	Main technical input
Gaiotto, Kapustin, Seiberg, Willett, “Generalized global symmetries”, JHEP 02 (2015) 172, arXiv:1412.5148	Block 1 target (Wk 1 seminar: §§2–3, §4.1, App. F; Wk 2: §§4.3, 5.2, App. B); Sem I Wks 14–15	§§1–5, 7.2 + Maxwell/ℤ_N examples	p-form symmetries as topological operators; SSB of 1-form symmetries; gauging with backgrounds.
Kapustin & Seiberg, “Coupling a QFT to a TQFT and duality”, JHEP 04 (2014) 001, arXiv:1401.0740	Block 1 support (Wk 2: §3)	§§1–3	Coupling a QFT to a TQFT; what “sum over backgrounds” does to the operator spectrum.
Freed, Moore, Segal, “The uncertainty of fluxes”, Commun. Math. Phys. 271 (2007) 247 [hep-th/0605198]; “Heisenberg groups and noncommutative fluxes”, Ann. Phys. 322 (2007) 236 [hep-th/0605200]	Wk 1 (F7, Problem 8⋆⋆)	statements	Electric and magnetic fluxes do not commute: the Heisenberg group of a $U (1)$ gauge theory on a spatial manifold.
Horowitz, “Exactly soluble diffeomorphism invariant theories”, Commun. Math. Phys. 125 (1989) 417	Wk 2	statements	BF theory as an exactly soluble topological field theory.
Maldacena, Moore, Seiberg, “D-brane charges in five-brane backgrounds”, JHEP 10 (2001) 005 [hep-th/0108152]	Wk 2	the BF section	Level- $N$ BF theory and its finite Hilbert space on a torus.
Banks & Seiberg, “Symmetries and strings in field theory and gravity”, Phys. Rev. D 83 (2011) 084019 [1011.5120]	Wk 2	§§2–4	$Z_{N}$ gauge theory as BF theory; discrete gauge symmetries and their charges.
Hofman & Iqbal, “Goldstone modes and photonization for higher form symmetries”, SciPost Phys. 6 (2019) 006 [arXiv:1802.09512]	Wk 3	statements	The photon as the Goldstone boson of a spontaneously broken 1-form symmetry.
Lake, “Higher-form symmetries and spontaneous symmetry breaking”, arXiv:1802.07747 (preprint)	Wk 3	statements	Goldstone theorem and Coleman–Mermin–Wagner bound for higher-form symmetries.
Tachikawa, “On gauging finite subgroups”, SciPost Phys. 8 (2020) 015 [arXiv:1712.09542]	Wk 4	§§1–2	Gauging a finite subgroup, the dual symmetry, and mixed anomalies.
Vafa, “Quantum symmetries of string vacua”, Mod. Phys. Lett. A 4 (1989) 1615	Wk 4 (historical note)	statements	The quantum (dual) symmetry of an orbifold.
Aharony, Seiberg, Tachikawa, “Reading between the lines of four-dimensional gauge theories”, JHEP 08 (2013) 115 [arXiv:1305.0318]	Wk 4 (seminar: §§1.1–1.3, 2.1, 2.3, 6.4); Sem I Wk 14	§§1–3	Line-operator spectra of SU(N) vs SU(N)/ℤ_N; genuine vs non-genuine operators.
Gaiotto, Kapustin, Komargodski, Seiberg, “Theta, time reversal, and temperature”, JHEP 05 (2017) 091 [arXiv:1703.00501]	Block 2 target (Wk 5: App. D.1)	§§1–3 + one appendix calculation	The ℤ_N^(1) × T mixed anomaly at θ = π and its phase-diagram consequences.
‘t Hooft, “Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking”, NATO Sci. Ser. B 59 (1980) 135 (Cargèse 1979)	Wk 5	the anomaly-matching argument	Anomaly matching with spectators.
Callan & Harvey, “Anomalies and fermion zero modes on strings and domain walls”, Nucl. Phys. B 250 (1985) 427	Wk 5	statements	Anomaly inflow from the bulk to defects.
Cheng & Seiberg, “Lieb–Schultz–Mattis, Luttinger, and ‘t Hooft — anomaly matching in lattice systems”, SciPost Phys. 15 (2023) 051 [arXiv:2211.12543]	Wk 5	statements	LSM constraints as lattice anomalies.
Else & Nayak, “Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge”, Phys. Rev. B 90 (2014) 235137 [arXiv:1409.5436]	Wks 5, 7	statements	The edge action of the symmetry as the SPT invariant.
Ogata, Tachikawa, Tasaki, “General Lieb–Schultz–Mattis type theorems for quantum spin chains”, Commun. Math. Phys. 385 (2021) 79 [arXiv:2004.06458]	Wk 5	statements	LSM theorems for chains with a projective symmetry per site.
Briegel & Raussendorf, “Persistent entanglement in arrays of interacting particles”, Phys. Rev. Lett. 86 (2001) 910 [quant-ph/0004051]	Wks 5, 7	statements	The cluster state.
Majumdar & Ghosh, J. Math. Phys. 10 (1969) 1388	Wk 5 (Problem)	statements	The Majumdar–Ghosh chain and its dimerized ground states.
‘t Hooft, “A property of electric and magnetic flux in nonabelian gauge theories”, Nucl. Phys. B 153 (1979) 141	Wk 6; Sem I Wk 14	§§1–4	Twisted boundary conditions on $T^{4}$ and the electric and magnetic flux sectors.
‘t Hooft, “Some twisted selfdual solutions for the Yang–Mills equations on a hypertorus”, Commun. Math. Phys. 81 (1981) 267	Wk 6	statements	Constant-curvature self-dual solutions with fractional instanton number.
Witten, “Large N chiral dynamics”, Ann. Phys. 128 (1980) 363	Wk 6	statements	θ-dependence at large N and the multibranch vacuum energy.
Witten, “Theta dependence in the large N limit of four-dimensional gauge theories”, Phys. Rev. Lett. 81 (1998) 2862 [hep-th/9807109]	Wk 6	statements	The branch structure of the vacuum energy at large N.
Lüscher, “Topology of lattice gauge fields”, Commun. Math. Phys. 85 (1982) 39	Wk 6	statements	The topological charge of lattice gauge fields.
Chen, Gu, Liu, Wen, “Symmetry protected topological orders and the group cohomology of their symmetry group”, Phys. Rev. B 87 (2013) 155114 [arXiv:1106.4772]	Wk 7	1d classification + statements	SPT classification by group cohomology.
Affleck, Kennedy, Lieb, Tasaki, Phys. Rev. Lett. 59 (1987) 799	Wk 7	statements	The AKLT chain: a valence-bond solid with spin-½ edges.
Haldane, Phys. Lett. A 93 (1983) 464; Phys. Rev. Lett. 50 (1983) 1153	Wk 7	statements	The Haldane gap of integer-spin chains.
den Nijs & Rommelse, Phys. Rev. B 40 (1989) 4709	Wk 7	statements	String order in the Haldane phase.
Pérez-García, Wolf, Sanz, Verstraete, Cirac, Phys. Rev. Lett. 100 (2008) 167202 [0802.0447]	Wk 7	statements	String order and symmetries in MPS: the virtual action of a symmetry.
Pollmann, Turner, Berg, Oshikawa, Phys. Rev. B 81 (2010) 064439 [0910.1811]	Wk 7	statements	Entanglement spectrum and the protection of the Haldane phase.
Chen, Gu, Wen, “Classification of gapped symmetric phases in one-dimensional spin systems”, Phys. Rev. B 83 (2011) 035107 [1008.3745]	Wk 7	statements	The MPS classification of 1d SPT phases by $H^{2} (G, U (1))$ .
Levin & Gu, Phys. Rev. B 86 (2012) 115109 [1202.3120]	Wk 7 seminar (§§I–III, V.A)	§§I–III, V.A	Braiding statistics approach to SPT phases; gauging the $Z_{2}$ SPT.
Raussendorf & Briegel, Phys. Rev. Lett. 86 (2001) 5188	Wk 7	statements	The cluster state as a resource.
Else, Schwarz, Bartlett, Doherty, Phys. Rev. Lett. 108 (2012) 240505 [1201.4877]	Wk 7	statements	SPT order and measurement-based computation.
Vishwanath & Senthil, Phys. Rev. X 3 (2013) 011016 [1209.3058]	Wk 7	statements	Bosonic SPT phases beyond group cohomology in 3+1d.
Dijkgraaf & Witten, Commun. Math. Phys. 129 (1990) 393	Wk 7	§6 (finite groups)	Topological gauge theories from group cocycles; the toric-code/double-semion dichotomy.
Lieb, Schultz, Mattis, Ann. Phys. 16 (1961) 407; Oshikawa, Phys. Rev. Lett. 84 (2000) 1535; Hastings, Phys. Rev. B 69 (2004) 104431 [cond-mat/0305505]	Wk 5	statements + flux-threading argument	LSM as a lattice anomaly; the theorem that makes anomalies concrete for spin chains.

Topological order and quantum information (Semester II Block 3 spine)

Reference	Course use	Required sections	Main technical input
Kitaev, “Fault-tolerant quantum computation by anyons”, Ann. Phys. 303 (2003) 2 [quant-ph/9707021]	Wk 2 seminar; Wk 8 target; Wk 10	the sections on toric codes, abelian anyons and materialized symmetry (§§1–3 of the arXiv text)	The toric code: stabilizers, anyons, fault tolerance.
Kitaev, “Anyons in an exactly solved model and beyond”, Ann. Phys. 321 (2006) 2 [cond-mat/0506438]	Wk 7 (App. E, anyon data); Wk 8 (App. E.4–E.5); Wk 10; Wk 11 (§§8.3–8.6, §9, App. E.1–E.2)	§§1–2 skim	The honeycomb model; anyon theory in its mature form (appendix as reference, not reading).
Kitaev & Preskill, Phys. Rev. Lett. 96 (2006) 110404 [hep-th/0510092]; Levin & Wen, Phys. Rev. Lett. 96 (2006) 110405 [cond-mat/0510613]	Wk 9	full (both are 4 pages)	Topological entanglement entropy, two constructions.
Kirillov & Balsam, “Turaev–Viro invariants as an extended TQFT”, arXiv:1004.1533	Wk 11	statements	The Levin–Wen models as Turaev–Viro state sums; the doubled content of a string net.
Laughlin, Phys. Rev. Lett. 50 (1983) 1395	Wk 10	statements	The ν = 1/3 state.
Arovas, Schrieffer, Wilczek, Phys. Rev. Lett. 53 (1984) 722	Wk 10	statements	Fractional statistics of the Laughlin quasiholes.
Wen, Phys. Rev. B 41 (1990) 12838	Wk 10	statements	Chiral edge states of fractional quantum Hall states.
Wen & Zee, Phys. Rev. B 46 (1992) 2290	Wk 10	statements	The K-matrix classification of abelian quantum Hall states.
Witten, “The Chern–Simons function and the quantum Hall effect”, to appear in Bull. Amer. Math. Soc. [arXiv:2609.21182]	Sem I Wk 12; Sem II Wk 10	§§1–4	The θ-term and the Chern–Simons function from a 4-manifold extension, integrality on spin manifolds, the integer Hall level and the emergent-field model of the fractional effect.
Witten, “Quantum field theory and the Jones polynomial”, Commun. Math. Phys. 121 (1989) 351	Wk 10	statements	Chern–Simons theory, Wilson lines and their framing.
Coste, Gannon, Ruelle, Nucl. Phys. B 581 (2000) 679 [hep-th/0001158]	Wk 10	statements	The modular data of finite-group quantum doubles.
Levin & Wen, “Fermions, strings, and gauge fields in lattice spin models”, Phys. Rev. B 67 (2003) 245316 [cond-mat/0302460]	Wk 8	statements	Anyon statistics from string operators: the T-junction argument.
Bais & Slingerland, “Condensate induced transitions between topologically ordered phases”, Phys. Rev. B 79 (2009) 045316 [arXiv:0808.0627]	Wk 8	statements	Rules for anyon condensation.
Castelnovo & Chamon, “Quantum topological phase transition at the microscopic level”, Phys. Rev. B 77 (2008) 054433 [arXiv:0707.2084]	Wk 11	statements	A deformed toric-code wave function whose topological entropy vanishes beyond a transition.
Hamma, Ionicioiu, Zanardi, Phys. Rev. A 71 (2005) 022315 [quant-ph/0409073]	Wk 9	statements	The bipartite entanglement of the toric code from its stabilizer group.
Bravyi & Kitaev, “Quantum codes on a lattice with boundary”, quant-ph/9811052	Wk 9	statements	The planar code with rough and smooth boundaries.
Bravyi, Hastings, Verstraete, Phys. Rev. Lett. 97 (2006) 050401 [quant-ph/0603121]	Wk 9	statements	Lieb–Robinson bounds and the generation of topological order.
Bravyi, Hastings, Michalakis, J. Math. Phys. 51 (2010) 093512 [1001.0344]	Wk 9	statements	Stability of topological order under local perturbations.
Honecker, Picco, Pujol, Phys. Rev. Lett. 87 (2001) 047201 [cond-mat/0010143]	Wk 9	the value $p_{c} = 0.1094 (2)$	The Nishimori point of the 2d random-bond Ising model.
Wang, Harrington, Preskill, Ann. Phys. 303 (2003) 31 [quant-ph/0207088]	Wk 9	the thresholds 0.0293(2) and 0.1031(1)	Toric-code thresholds with and without measurement errors.
Zou & Haah, Phys. Rev. B 94 (2016) 075151 [1604.06101]	Wk 9	statements	Spurious topological entanglement entropy.
Levin & Wen, “String-net condensation: a physical mechanism for topological phases”, Phys. Rev. B 71 (2005) 045110 [cond-mat/0404617]	Wk 11 target	§§1–4 + ℤ₂ example	String-net condensation; F-symbols; emergent gauge theory.
Wen, Int. J. Mod. Phys. B 4 (1990) 239; Wen & Niu, Phys. Rev. B 41 (1990) 9377	Wk 2 (optional), Wk 8 context, Wk 10 seminar	statements	Topological order named and defined; GSD on higher genus.
Chen, Gu, Wen, Phys. Rev. B 82 (2010) 155138 [arXiv:1004.3835]	Wk 9	§§II–V	Phases as local-unitary equivalence classes; long-range entanglement.
Dennis, Kitaev, Landahl, Preskill, J. Math. Phys. 43 (2002) 4452 [quant-ph/0110143]	Wk 9	§§I, III.A–B, IV	The toric code as a quantum memory; error models and thresholds.
Hansson, Oganesyan, Sondhi, “Superconductors are topologically ordered”, Ann. Phys. 313 (2004) 497 [cond-mat/0404327]	Wks 2, 3 (seminar); Sem I Wk 14	§§I–IV, V.A–B (Roman numbering)	Superconductors are topologically ordered; the 1-form-symmetry reading of BCS.
Trebst, Werner, Troyer, Shtengel, Nayak, “Breakdown of a topological phase: quantum phase transition in a loop gas model with tension”, Phys. Rev. Lett. 98 (2007) 070602 [cond-mat/0609048]; Tupitsyn, Kitaev, Prokof’ev, Stamp, “Topological multicritical point in the toric code and 3D gauge Higgs models”, Phys. Rev. B 82 (2010) 085114 [arXiv:0804.3175]	Wk 8 + write-up topic 2; Sem I Wks 13–14	phase diagrams	The perturbed toric code = the Fradkin–Shenker diagram, numerically mapped.

The modern lattice synthesis and condensation defects (Semester II Blocks 4–5 spine)

Reference	Course use	Required sections	Main technical input
Sulejmanpasic & Gattringer, “Abelian gauge theories on the lattice: θ-terms and compact gauge theory with(out) monopoles”, Nucl. Phys. B 943 (2019) 114616 [arXiv:1901.02637]	Wk 12; Sem I Wk 12	§§1–3	Monopole-free compact lattice QED; well-defined lattice θ-terms.
Gorantla, Lam, Seiberg, Shao, “A modified Villain formulation of fractons and other exotic theories”, J. Math. Phys. 62 (2021) 102301 [arXiv:2103.01257]	Wk 2 (App. C.2, the BF dictionary); Wk 12 target (§1.2, Apps. B.1, C.1)	Villain sections (skip fracton applications on first pass)	The modified Villain systematics: exact dualities, exact higher-form symmetries, exact anomalies on the lattice.
Chen & Tata, “Higher cup products on hypercubic lattices: application to lattice models of topological phases”, J. Math. Phys. 64 (2023) 091902 [arXiv:2106.05274]	Wks 6, 12 reference	as needed	Higher cup products on hypercubic lattices; the sign conventions conventions adopts.
Koide, Nagoya, Yamaguchi, PTEP 2022 (2022) 013B03 [2109.05992]	Wk 13 (statement); Wk 14 (optional)	abstract	Non-invertible topological defects in 4d $Z_{2}$ gauge theory.
Fröhlich, Fuchs, Runkel, Schweigert, Phys. Rev. Lett. 93 (2004) 070601 [cond-mat/0404051]	Wk 13 (history)	statements	Kramers–Wannier duality from conformal defects.
Seiberg & Shao, SciPost Phys. 16 (2024) 064 [2307.02534]	Wk 13	statements	Majorana chain and Ising model: non-invertible translations, anomalies and emanant symmetries.
Aasen, Mong, Fendley, “Topological defects on the lattice I: the Ising model”, J. Phys. A 49 (2016) 354001 [arXiv:1601.07185]	Wk 13 target	§§1–4	The Kramers–Wannier duality defect on the lattice Ising model.
Burnell, “Anyon condensation and its applications”, Ann. Rev. Condens. Matter Phys. 9 (2018) 307 [arXiv:1706.04940]	Wk 15 (reading list, open problem 10 of Wk 14)	statements	Anyon condensation beyond the abelian case.
Nandkishore & Hermele, “Fractons”, Ann. Rev. Condens. Matter Phys. 10 (2019) 295 [arXiv:1803.11196]	Wk 15 (reading list, open problem 9 of Wk 14)	statements	Fracton phases.
Seiberg & Shao, “Exotic ℤ_N symmetries, duality, and fractons in 3+1-dimensional quantum field theory”, SciPost Phys. 10 (2021) 003 [arXiv:2004.06115]	Wk 15 (reading list, open problem 9 of Wk 14)	statements	Exotic subsystem symmetries and their lattice models.
Tantivasadakarn, Thorngren, Vishwanath, Verresen, “Long-range entanglement from measuring symmetry-protected topological phases”, Phys. Rev. X 14 (2024) 021040 [arXiv:2112.01519]	Wk 15 (reading list, open problem 11 of Wk 14)	statements	Gauging by measurement.
Guimaraes, “Finite-cost currents at higher-gauging walls in four-dimensional ℤ_N gauge theory”, manuscript in preparation (version 25, 2026-09-20; not submitted)	Wk 14 target + master-project	§§1–9 and the appendices	The group’s manuscript: the higher-gauging wall, its endpoint currents, the clock dual and the endpoint tension.
Choi, Córdova, Hsin, Lam, Shao, “Non-invertible condensation, duality, and triality defects in 3+1 dimensions”, Commun. Math. Phys. 402 (2023) 489 [arXiv:2204.09025]	Wk 14	statements	Condensation defects in 3+1d.
Bah, Leung, Waddleton, “On the physics of higher condensation defects”, JHEP 09 (2026) 272 [arXiv:2506.04346]	Wk 14	statements	The four-dimensional subgroup condensation defect with its worldvolume symmetries and fusion data; the construction the manuscript names as closest to its wall.
Córdova, Costa, Hsin, “Non-invertible symmetries as condensation defects in finite-group gauge theories”, arXiv:2412.16681	Wk 14 (optional)	statements	Lattice gauging interfaces.
Hofmeier, Pimenta, Cao, “Lattice gauging interfaces and noninvertible defects in higher dimensions”, arXiv:2605.12601	Wk 14 (optional)	statements	Lattice gauging interfaces.
Xue, Yang, Zhang, “On gauging finite symmetries by higher gauging condensation defects”, JHEP 08 (2026) 179 [arXiv:2512.22440]	Wk 14 (optional)	statements	Gauging by condensation defects.
Choi, Sanghavi, Shao, Zheng, “Non-invertible and higher-form symmetries in 2+1d lattice gauge theories”, SciPost Phys. 18 (2025) 008 [arXiv:2405.13105]	Wk 14 (optional)	statements	Lattice duality defects in 2+1d gauge theories.
Ukawa, Windey, Guth, “Dual variables for lattice gauge theories and the phase structure of Z(N) systems”, Phys. Rev. D 21 (1980) 1013; Nguyen, Sulejmanpasic, Ünsal, Phys. Rev. Lett. 134 (2025) 141902 [arXiv:2401.04800]	Wk 14 (optional)	statements	The phase structure of ℤ_N gauge theories.
Janke & Villanova, Nucl. Phys. B 489 (1997) 679 [hep-lat/9612008]; Karsch & Stickan, Phys. Lett. B 488 (2000) 319 [hep-lat/0007019]; Xu, Sun, Lv et al., Phys. Rev. B 100 (2019) 064525 [1908.10990]; Ditzian et al., Phys. Rev. B 22 (1980) 2542 and Todoroki et al. [cond-mat/0207665] (these two as the manuscript cites them, not checked on INSPIRE)	Wk 14 (optional)	critical couplings	Three-dimensional clock and Potts models.
Grigorio, Guimaraes, Oliveira et al., “U(1) effective confinement theory from SU(2) restricted gauge theory via the Julia–Toulouse approach”, Phys. Lett. B 697 (2011) 392 [arXiv:1010.6215]	Wk 14	statements	The group’s Julia–Toulouse treatment of restricted SU(2), as the manuscript cites it.
Roumpedakis, Seifnashri, Shao, “Higher gauging and non-invertible condensation defects”, Commun. Math. Phys. 401 (2023) 3043 [arXiv:2204.02407]	Wk 13–14 target	§§1–3 + condensation-defect construction	Higher gauging; condensation defects; projector fusion — the framework the manuscript takes as prior work.
Choi, Córdova, Hsin, Lam, Shao, Phys. Rev. D 105 (2022) 125016 [arXiv:2111.01139]; Kaidi, Ohmori, Zheng, Phys. Rev. Lett. 128 (2022) 111601 [arXiv:2111.01141]	Wks 12–13 (statement)	intros	Non-invertible duality defects in 3+1d from half-space gauging.
Julia & Toulouse, J. Physique Lett. 40 (1979) L-395	Sem I Wk 11; Wk 14	full (it is 4 pages)	The original: defect condensation changes the effective field content.
Quevedo & Trugenberger, Nucl. Phys. B 501 (1997) 143 [hep-th/9604196]	Sem I Wk 11; Wk 14	§§1–3	The JTA in field-theory form; rank-changing condensation — see julia-toulouse-mechanism.
The group’s JTA series: Grigorio, Guimaraes, Wotzasek, Phys. Lett. B 674 (2009) 213 [0808.3698] (monopoles with a Chern–Simons term); Grigorio, Guimaraes, Rougemont, Wotzasek, Phys. Lett. B 690 (2010) 316 [0908.0370] (dual approaches to defect condensation); Grigorio, Guimaraes, Rougemont, Wotzasek, JHEP 08 (2011) 118 [1102.3933] (confinement and brane symmetry); Grigorio, Guimaraes, Rougemont, Wotzasek, Zarro, Phys. Rev. D 86 (2012) 027705 [1202.3798] (the BF theory as an electric JT condensate); Guimaraes, Rougemont, Wotzasek, Zarro, Phys. Rev. D 86 (2012) 125039 [1209.2751] (the bosonized Schwinger model); Guimaraes, Rougemont, Wotzasek, Zarro, Phys. Lett. B 723 (2013) 422 [1209.3073] (electric condensate and magnetic confinement); Grigorio, Guimaraes, Rougemont, Wotzasek, Zarro, Phys. Rev. D 88 (2013) 065009 [1307.1035] (Chern–Simons term in a dual Josephson junction)	Wks 9, 11, 14	selected	The confinement-duality line this course descends from. Cite papers individually: “PRD 86” alone is ambiguous. In the BF language, level-one $B \land d a$ with the original photon is the electric condensate (PRD 86 027705, PLB 723); the magnetic condensate is the massive Kalb–Ramond form, dual to $B \land d \tilde{a}$ .

Block A additions (2026-07-07 notes rewrite)

References introduced by the full Semester I Block A lecture notes, per the citation gate of the note-quality-template.

Reference	Used in	What for
Kosterlitz, J. Phys. C 7 (1974) 1046	Wk 4	the RG flow equations
Nelson & Kosterlitz, Phys. Rev. Lett. 39 (1977) 1201	Wks 1, 4	the universal stiffness jump
Bishop & Reppy, Phys. Rev. Lett. 40 (1978) 1727	Wks 1, 4	torsional-oscillator measurement of the jump
Kardar, Statistical Physics of Fields, CUP 2007, ch. 8 (the sections on topological defects in the XY model and on the renormalization group of the Coulomb gas)	Wk 4	RG derivation in matching conventions
Minnhagen, Rev. Mod. Phys. 59 (1987) 1001	Wk 4	Coulomb-gas review; first-order caveat at large fugacity
Fröhlich & Spencer, Comm. Math. Phys. 81 (1981) 527	Wk 3	rigorous existence of the BKT transition via the Coulomb gas
Mermin & Wagner, Phys. Rev. Lett. 17 (1966) 1133; Hohenberg, Phys. Rev. 158 (1967) 383	Wk 1	no continuous-symmetry breaking in $d \leq 2$
Spitzer, Principles of Random Walk, 2nd ed., Springer 1976, §15	Wk 1	lattice Green function asymptotics (the constant κ)
Onsager, Phys. Rev. 65 (1944) 117	Wk 4	exact Ising solution (context for Kramers–Wannier)
Peierls, Proc. Camb. Phil. Soc. 32 (1936) 477	Wk 4	existence of the Ising transition (duality only locates it)
Chui & Weeks, Phys. Rev. B 14 (1976) 4978	Wk 3	roughening ↔ BKT correspondence for the height model
Chaikin & Lubensky, Principles of Condensed Matter Physics, CUP 1995, §9	Wk 1	vortices and stiffness in laboratory language

Additions from the 2026-09-27 review

References that the Semester I notes use or quote but that were missing here, all verified against INSPIRE on 2026-09-27.

Reference	Used in	What for
Hasenbusch, J. Phys. A 38 (2005) 5869 [cond-mat/0502556]	Wks 1, 3, 4	bare critical coupling of the cosine XY model, $β_{c} \approx 1.12$
Janke & Nather, Phys. Rev. B 48 (1993) 7419	Wks 1, 3, 4	bare critical coupling of the Villain XY model, $β_{c} \approx 0.75$
Kogut, “The lattice gauge theory approach to quantum chromodynamics” (printed title; INSPIRE lists “A review of the lattice gauge theory approach…”), Rev. Mod. Phys. 55 (1983) 775	Wks 6, 7	strong-coupling methods and roughening (§§IV.A, V.A, V.C)
‘t Hooft, “Gauge fields with unified weak, electromagnetic, and strong interactions”, EPS International Conference on High-Energy Physics, Palermo, 23–28 June 1975, p. 1225	Wk 11	the dual-superconductor proposal
Witten, Phys. Lett. B 86 (1979) 283	Wk 12	the Witten effect
Wilczek, Phys. Rev. Lett. 58 (1987) 1799	Wk 12	axion electrodynamics
Osterwalder & Seiler, “Gauge field theories on the lattice”, Ann. Phys. 110 (1978) 440	Wks 10, 13	the convergent expansion behind Higgs–confinement complementarity
Svetitsky & Yaffe, Nucl. Phys. B 210 (1982) 423	Wks 10, 14	universality of the deconfinement transition
Göpfert & Mack, Commun. Math. Phys. 82 (1982) 545 (the volume spans 1981–82; INSPIRE lists 1981, the journal header 1982; Villain action, Theorem 1, Corollary 2, eq. (1.8a) for the Debye mass)	Wks 9–10	confinement of static charges in 3d $U (1)$ lattice gauge theory at all couplings
Fröhlich & Spencer, Commun. Math. Phys. 83 (1982) 411	Wk 11	the massless (Coulomb) phase of 4d abelian lattice gauge theory
Arnold, Bunk, Lippert, Schilling, “Compact QED under scrutiny: it’s first order”, Nucl. Phys. B Proc. Suppl. 119 (2003) 864 [hep-lat/0210010]	Wk 11	the order of the 4d Wilson-action transition, $β_{T} = 1.0111331 (21)$
‘t Hooft, “Topology of the gauge condition and new confinement phases in nonabelian gauge theories”, Nucl. Phys. B 190 (1981) 455	Wk 11	abelian projection
Seiberg & Witten, “Electric–magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang–Mills theory”, Nucl. Phys. B 426 (1994) 19; Erratum 430 (1994) 485 [hep-th/9407087]	Wk 11	a controlled realization of monopole condensation
Cardy, “Duality and the θ parameter in abelian lattice models”, Nucl. Phys. B 205 (1982) 17	Wk 12	oblique confinement on the lattice
Witten, “On S-duality in abelian gauge theory”, Selecta Math. 1 (1995) 383 [hep-th/9505186]	Wk 12	the SL(2,ℤ) action on abelian gauge theory
Qi, Hughes, Zhang, “Topological field theory of time-reversal invariant insulators”, Phys. Rev. B 78 (2008) 195424 [0802.3537]	Wk 12	θ = π in topological insulators
Zyuzin & Burkov, “Topological response in Weyl semimetals and the chiral anomaly”, Phys. Rev. B 86 (2012) 115133 [1206.1868]	Wk 12	the axion response of Weyl semimetals
Vazifeh & Franz, “Electromagnetic response of Weyl semimetals”, Phys. Rev. Lett. 111 (2013) 027201 [1303.5784]	Wk 12	absence of the chiral magnetic effect in equilibrium
Braga, Guimaraes, Paganelly, “Multivalued fields and monopole operators in topological superconductors”, Ann. Phys. 419 (2020) 168245 [1812.01705]; Chrispim, Bruni, Guimaraes, “Massive photon propagator in the presence of axionic fluctuations”, Phys. Rev. B 103 (2021) 165120 [2012.00184]	Wk 12	the group’s condensed-matter line
Fredenhagen & Marcu, “Charged states in ℤ₂ gauge theories”, Commun. Math. Phys. 92 (1983) 81; “A confinement criterion for QCD with dynamical quarks”, Phys. Rev. Lett. 56 (1986) 223	Wk 13	the Fredenhagen–Marcu order parameter
Fröhlich, Morchio, Strocchi, “Higgs phenomenon without symmetry breaking order parameter”, Nucl. Phys. B 190 (1981) 553	Wk 13	gauge-invariant description of the Higgs phase
Jongeward, Stack, Jayaprakash, Phys. Rev. D 21 (1980) 3360	Wk 13	Monte Carlo phase diagram of the ℤ₂ gauge–Higgs model
Griffiths, J. Math. Phys. 8 (1967) 478; Ginibre, Commun. Math. Phys. 16 (1970) 310	Wk 13	correlation inequalities behind $⟨ W ⟩ \geq (tanh κ)^{∣ C ∣}$
Kotecký & Preiss, Commun. Math. Phys. 103 (1986) 491	Wk 13	the convergence criterion of the polymer expansion
Somoza, Serna, Nahum, “Self-dual criticality in three-dimensional ℤ₂ gauge theory with matter”, Phys. Rev. X 11 (2021) 041008 [2012.15845]	Wk 13	the multicritical point on the self-dual line
Kajantie, Laine, Rummukainen, Shaposhnikov, Phys. Rev. Lett. 77 (1996) 2887 [hep-ph/9605288]; Rummukainen, Tsypin, Kajantie, Nucl. Phys. B 532 (1998) 283 [hep-lat/9805013]	Wk 13	the endpoint of a Higgs first-order line and its Ising class
Polyakov, “Thermal properties of gauge fields and quark liberation”, Phys. Lett. B 72 (1978) 477; Susskind, “Lattice models of quark confinement at high temperature”, Phys. Rev. D 20 (1979) 2610	Wk 14	the Polyakov loop as the order parameter of deconfinement
Greensite, An Introduction to the Confinement Problem, Lecture Notes in Physics 821, Springer 2011 (book, not checked)	Wk 14	center symmetry and confinement criteria
Blöte & Deng, “Cluster Monte Carlo simulation of the transverse Ising model”, Phys. Rev. E 66 (2002) 066110	Wk 7	the critical point $(K /Γ)_{c} \approx 3.044$ of the $2 + 1$ d $Z_{2}$ gauge theory through its dual transverse-field Ising model
NIST Digital Library of Mathematical Functions, §28.8 (Mathieu functions, asymptotics for large q), https://dlmf.nist.gov/28.8	Wk 7	the one-plaquette tunnelling splitting
Drouffe & Itzykson, “Lattice gauge fields”, Phys. Rep. 38 (1978) 133	Wk 6	strong-coupling and character-expansion methods
Ferrenberg, Xu, Landau, “Pushing the limits of Monte Carlo simulations for the 3d Ising model”, Phys. Rev. E 97 (2018) 043301 [arXiv:1806.03558]	Wks 5, 14	the 3d Ising critical coupling $K_{c} = 0.221654626 (5)$ , hence $β_{c}$ of 3d $Z_{2}$ gauge theory
Amit, Goldschmidt, Grinstein, “Renormalization group analysis of the phase transition in the 2D Coulomb gas, sine-Gordon theory and XY model”, J. Phys. A 13 (1980) 585	Wk 4	the Kosterlitz flow beyond leading order
Pelissetto & Vicari, “Renormalization-group flow and asymptotic behaviors at the Berezinskii–Kosterlitz–Thouless transitions”, Phys. Rev. E 87 (2013) 032105 [arXiv:1212.2322]	Wk 4	canonical form of the next-order flow; finite-size stiffness

Committed 2026-07-01 as part of the Phase-1 scaffold; Block A additions appended 2026-07-07; corrections and additions from the 2026-09-27 review appended the same day. Per-week reading pointers live in the block skeletons.

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Appendix — Bibliography and Paper Map