Bibliography and source versions — Geometric QCD

Bibliography and source versions

This map separates supplied lecture pages, primary research sources, and instructional bridges. Metadata and versions were checked on 4 October 2026. Publication is evidence of provenance, not an independent verification of every argument.

Core source

Alexander Migdal, IAS lectures, 27 March 2026, 142 pages. The supplied PDF is the main source for the course’s reconstruction. Page numbers refer to PDF/slide pages, which agree. The page map covers all 142 pages.

Alexander Migdal, Geometric QCD I: The Hodge-Dual Surface and Quark Confinement. arXiv:2511.13688, version 7 dated 16 February 2026; Nuclear Physics B 1025 (2026), 117380, publisher DOI. Use for the proposed geometric and variational construction. III.5 tests the formulas actually supplied in the lecture PDF.

Alexander Migdal, Geometric QCD II: The Confining Twistor String and Meson Spectrum. arXiv:2602.21129v4, dated 23 March 2026; Nuclear Physics B 1026 (2026), 117424, publisher DOI. Use Appendix C for the reported finite-system diagnostics and the spectral sections for the fit protocol. The IAS fourth-order tensor and the Appendix C representative differ; II.5 preserves this discrepancy.

Source computational notebook: MLEAlgebraic.nb, cited by Part II. This course does not claim to have executed or certified that notebook. A research reproduction must freeze its inputs and export the equations and certificate.

Module 1

• Primary: G. ‘t Hooft, A planar diagram theory for strong interactions, Nuclear Physics B 72 (1974), 461–473. Author-hosted paper, DOI. Read for ribbon topology and color scaling.
• Primary: Yu. M. Makeenko and A. A. Migdal, Exact equation for the loop average in multicolor QCD, Physics Letters B 88 (1979), 135–137. Publisher record. Read for the original loop-equation context; compare conventions with I.5.
• Gentler: the matrix/Gaussian and Fourier/distribution bridges in this course.
• Research: IAS pp. 20–42; define a crossing regulator and operator basis before comparing renormalized equations.

Module 2

• Primary: IAS pp. 43–65 and Part II’s momentum-loop discussion and Appendix C.
• Primary background: A. Migdal, Second Quantization of the Wilson Loop, arXiv:hep-th/9411100. Use for the operator-representation context.
• Gentler: II.4’s rectangle, II.5’s complete model system, and II.7’s free-word basis.
• Research: the source notebook and exact rational matrix export. Source dimensions alone are not a reproduced rank computation.

Module 3

• Primary: IAS pp. 66–91 and Part I’s proposed surface construction.
• Gentler: the forms/complex-analysis bridge and III.5’s circle and ellipse.
• Research: compare the tensor definition, boundary correspondence, area variation, and functional domain before claiming a zero mode. General names such as uniformization or a bridge principle do not replace their hypotheses and a calculation for this surface.

Module 4

• Primary: IAS pp. 92–110 and Part II’s surface-fermion construction.
• Instructional background: P. Ginsparg, Applied Conformal Field Theory, arXiv:hep-th/9108028. Use for two-dimensional fermions and conformal methods; its conventions must be translated.
• Gentler: the Grassmann bridge, IV.2’s coframe calculation, and IV.6’s test-function proof.
• Research: a regulated operator with its boundary domain, full determinant normalization, cancellation map, and contact matching.

Module 5

• Primary: IAS pp. 111–142 and Part II’s spectral construction.
• Primary comparison: E. Witten, Perturbative Gauge Theory As A String Theory In Twistor Space, arXiv:hep-th/0312171. This is the topological B-model proposal used for the limited comparison in V.4.
• Primary chiral framework: R. Kaiser and H. Leutwyler, Large $N_c$ in chiral perturbation theory, arXiv:hep-ph/0007101. Use to distinguish a model’s pion limitation from a general statement about the planar limit.
• Gentler: V.5’s explicit surface, V.6’s stationary equations, and V.7’s threshold expansion.
• Research data: a fit audit must name the exact Particle Data Group edition and preserve its selected state table. No current mass values have been silently substituted for the source fit.

What was checked

The revision checked primary records, the supplied slide equations, and the explicit model calculations recorded in the validation report. It did not perform a complete line-by-line certification of both research papers, a new nonperturbative QCD proof, a notebook reproduction of the eighth-order system, or a refit of all meson data.