Geometric QCD: a critical course on Migdal’s IAS lectures
Written by AI assistants under the scientific and pedagogical supervision of Marcelo S. Guimarães; see ai-authorship for the division of labour and the models involved.
Edition 2.0 · 4 October 2026. Five modules and 35 mini-lectures develop the loop equations, momentum variables, proposed surface construction, Majorana theory, and twistor spectrum. The course follows the explanatory standard of the AdS/CFT and AQFT dossiers: a physical question, necessary definitions, a reproducible calculation, interpretation, and explicit limits.
Start with the syllabus. Each note has classroom, self-study, and research routes, a worked laboratory, four problems, and answer checkpoints. The full course contains 140 problems with answers or completion guides.
The research proposal is taught critically. The revision corrects mathematical transcription and reasoning errors and identifies a further inconsistency in the literal extended-surface formula. The circular example in III.5 fails the asserted self-duality test. The subsequent QCD construction is therefore presented conditionally; this course does not certify a solution of planar QCD.
Course modules
- Loop calculus and the Makeenko–Migdal equation: ordered transport, point splitting, color algebra, perturbative checks, and contact singularities.
- Momentum loop space: finite Fourier models, closure, ordered integrals, tensor bases, rank certificates, and free-word representations.
- The proposed Hodge-dual vacuum: conditional zero modes, additivity, harmonic extension, conformality, explicit tensor tests, and OPE matching.
- Surface Majorana fermions: quadratic forms, spin geometry, determinants, local cancellation, contact normalization, and RG scaling.
- Twistors and the proposed spectrum: a finite Jacobian, radial weights, a variational problem, rotating surfaces, stationary phase, and a fit audit.
Study and teaching materials
- Prerequisite bridges and conventions.
- Notation and glossary.
- Collected exercises and checkpoints.
- Bibliography and source versions, 142-page source map, and claim status.
Sources
The main supplied source is Alexander Migdal’s 142-page IAS lecture PDF, dated 27 March 2026.
Wiki connections. Wilson loop · large-N factorization · confinement · confinement, duality, and topological defects