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Created basic outline with some important connections. Yang-Mills measure, after all the main concept which makes this special case interesting, and references will be added later.
Edit: Crosslinked D=2 Yang-Mills theory on related pages: D=2 QCD, D=4 Yang-Mills theory, D=5 Yang-Mills theory.
where you had a link to quantization I made it point to charge quantization instead
where it said “Chern-Weil theory implies” I expanded to “Chern-Weil theory implies that the first Chern class of the gauge bundle is:”
the section “Application to the 2-sphere” is lacking, I find, a sentence connecting back to the previous section. To this end, I have given your first display math environment the label “FirstChernClassByIntegration”, so that you can refer to this by typing “(eq:FirstChernClassByIntegration)”
apart from this I made some cosmetic edits here and there
beware that our Instiki parser demands more whitespace than ordinary LaTeX:
it renders “d_AA” like “d_\mathrm{AA}” — one needs to type “d_A A” to get the intended result (which may be a nuisance, but the latter form is also easier to parse by humans)
Thanks for the additions! I’ve also noticed “d_AA”, but then you already started editing the page. The section of the sphere will definitely get some expansion and connection (pun not intended). But what was wrong about putting D=4 Yang-Mills theory and D=5 Yang-Mills theory into related concepts?
I didn’t remove anything from “Related concepts”. Maybe our edits confliced, and I accidentally overwrote an edit of yours, sorry. Please put it back in, if you can.
Added:
The original reference:
Further developments:
Ninoslav E. Bralić, Exact computation of loop averages in two-dimensional Yang-Mills theory, Phys. Rev. D 22:12 (1980), 3090–3103. doi:10.1103/PhysRevD.22.3090.
V. A. Kazakov, I. K. Kostov, Non-linear strings in two-dimensional U(∞) gauge theory, Nuclear Physics B 176:1 (1980), 199–215. doi
Leonard Gross, Christopher King, Ambar Sengupta, Two dimensional Yang-Mills theory via stochastic differential equations, Annals of Physics 194:1 (1989), 65–112. doi
B. Ye. Rusakov, LOOP AVERAGES AND PARTITION FUNCTIONS IN U(N) GAUGE THEORY ON TWO-DIMENSIONAL MANIFOLDS, Modern Physics Letters A 5:9 (1990), 693–703. doi.
Dana S. Fine, Quantum Yang-Mills on the two-sphere, Communications in Mathematical Physics 134 (1990), 273–292. doi.
Dana S. Fine, Quantum Yang-Mills on a Riemann surface, Communications in Mathematical Physics 140 (1991), 321–338. doi.
Ambar Sengupta, The Yang-Mills measure for , Journal of Functional Analysis 108:2 (1992), 231–273. doi
Ambar Sengupta, Quantum Gauge Theory on Compact Surfaces, Annals of Physics 221:1 (1993), 17–52. doi
Matthias Blau, George Thompson, QUANTUM YANG-MILLS THEORY ON ARBITRARY SURFACES, International Journal of Modern Physics A 7:16 (1992), 3781–3806. doi.
One more:
more pointers
Edward Witten. On quantum gauge theories in two dimensions. Commun.Math. Phys. 141, 153–209 (1991). (doi).
Stefan Cordes, Gregory Moore, Sanjaye Ramgoolam. Lectures on 2D Yang-Mills Theory, Equivariant Cohomology and Topological Field Theories (1994). (hep-th/9411210).
David Gross. Two Dimensional QCD as a String Theory (1992). (hep-th/9212149)
David Gross, Washington Taylor, “Two-dimensional QCD is a string theory,” Nucl. Phys. B400 (1993). (hep-th/9301068).
David Gross, Washington Taylor, “Twists and Wilson loops in the string theory of two-dimensional QCD,” Nucl. Phys. B 403 (1993) 395-452. (hep-th/9303046).
Petr Hořava. Topological Strings and QCD in Two Dimensions (1993). (hep-th/9311156).
Petr Hořava. Topological Rigid String Theory and Two Dimensional QCD (1995). (hep-th/9507060).
Mendel Nguyen, Yuya Tanizaki, Mithat Ünsal. Non-invertible 1-form symmetry and Casimir scaling in 2d Yang-Mills theory (2021). (arXiv:2104.01824).
Tony Pantev, Eric Sharpe. Decomposition and the Gross-Taylor string theory (2023). (arXiv:2307.08729).
Richard Wedeen. Volume-Dependent Field Theories (2024). (arXiv:2402.06691).
Notice the separate entry D=2 QCD.
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