Primary bibliography

Selection updated: 24 October 2026. This is an editorial date. Consult each source record for the actual inspection date and reading depth.

Download the versioned BibTeX collection. Use the exact source versions and locators linked in each dossier when tracing a claim. Journal metadata, source reading and technical assessment are separate facts. This is a focused starting collection rather than a comprehensive literature survey.

First establish the question

Arthur Jaffe and Edward Witten — Quantum Yang–Mills Theory. The official problem description. Begin with the problem statement, then return to its discussion of axioms and construction as the course supplies the necessary bridges.

Clay Mathematics Institute — Yang–Mills & the Mass Gap. The institutional status page. Use it for the problem’s official status; use the Jaffe–Witten description for the mathematical target.

Rigorous construction and confinement

Before comparing methods, use the source notation crosswalk. It derives action and unit translations instead of matching symbol names.

Tadeusz Bałaban — Large field renormalization. II. Localization, exponentiation, and bounds for the R operation. Communications in Mathematical Physics 122 (1989), 355–392. Read the conditional ultraviolet-stability result first. Keep the quantity being bounded and the original theorem assumptions beside the argument.

Sourav Chatterjee — A probabilistic mechanism for quark confinement. Communications in Mathematical Physics 385 (2021), 1007–1039. Start with Definitions 2.1 and 2.3 and Theorems 2.2 and 2.4. The dossier distinguishes the premises and conclusions.

Sky Cao, Ron Nissim, and Scott Sheffield — Dynamical approach to area law for lattice Yang–Mills. Source version v2, 28 September 2025. Read Definition 1.4 before Theorem 1.6 so that the coupling normalization is unambiguous. Reading guide.

Ilya Chevyrev and Hao Shen — Uniqueness of gauge covariant renormalisation of stochastic 3D Yang–Mills–Higgs. Archive for Rational Mechanics and Analysis 250 (2026), article 11. Start with §1.2 and Theorem 1.6 after the distributions bridge. Scope guide.

Positivity and the loop hierarchy

Yuanhong Guo, Zeyu Li, Gang Yang, and Guorui Zhu — Bootstrapping SU(3) Lattice Yang–Mills Theory. JHEP 12 (2025), 033. Compare the positivity conditions in §3 before reading applications. The dossier keeps the dimensional restriction visible.

Xizhe Liu and Gang Yang — Direct and Indirect Loop Equations in Lattice Yang–Mills Theory. Source version v2. Read §5.1 for the elimination problem, then return to the constructions in §3. Algebraic entry point.

Spectra and reproducible comparison

Andreas Athenodorou and Michael Teper — SU(N) gauge theories in 3+1 dimensions: glueball spectrum, string tensions and topology. JHEP 12 (2021), 082. Read §2.2–2.3 before the continuum spectra in §5.5. Use the benchmark protocol to preserve conventions and uncertainties.

Calculable confinement mechanisms

Mithat Ünsal and Laurence G. Yaffe — Center-stabilized Yang–Mills theory: confinement and large N volume independence. Physical Review D 78 (2008), 065035. Identify the deformation and hierarchy of scales before following the mechanism.

Yui Hayashi, Yuya Tanizaki, and Mithat Ünsal — Center-vortex semiclassics with nonminimal ‘t Hooft fluxes. JHEP 02 (2026), 126. Read with the geometry and twist explicitly recorded. The joint semiclassical dossier explains how to compare the two settings.

Foundations and mathematical bridges

Konrad Osterwalder and Robert Schrader — Axioms for Euclidean Green’s functions. Communications in Mathematical Physics 31 (1973), 83–112. Read together with Axioms for Euclidean Green’s functions II, CMP 42 (1975), 281–305. The second paper extends and corrects the first. Reflection positivity is one part of a reconstruction theorem, not a substitute for all its hypotheses. Reconstruction guide.

Martin Lüscher — Properties and uses of the Wilson flow in lattice QCD. Source version v3, 27 January 2014. Equation (1.3), Appendix A and equation (3.3) supply the plaquette-counting, generator and flow-scale conventions used in the crosswalk. The flow parameter is not physical time.

Ajay Chandra, Ilya Chevyrev, Martin Hairer and Hao Shen — Stochastic quantisation of Yang-Mills-Higgs in 3D. Source version v2, 15 April 2024; Inventiones mathematicae 237 (2024), 541–696. Use it for the setting behind the stochastic method guide, preserving local existence and possible blow-up qualifications. A bibliographic entry does not establish that the entire proof was read.

David Tong — Gauge Theory lecture notes. Author-hosted 2018 teaching text accessed 24 October 2026, without a numbered revision identifier in this citation. Sections 2.1.1 and 2.6.2 support recovery of normalization and global-group background. These are teaching material; exact new research claims should be traced to their original papers.

A reading habit that scales

For every source, write three sentences: what is assumed, what is established, and what remains to reach the four-dimensional target. Keep publication status on a separate line. If a proof invokes another theorem, follow its hypotheses before borrowing its conclusion.

The research-reading lesson develops this practice. A bibliography is a route into the arguments; inclusion here is not a claim that the site has independently verified every proof or computation.