Lectures on 2D yang-mills theory, equivariant cohomology and topological field theories
Open accessAbstract
These are expository lectures reviewing (1) recent developments in two-dimensional Yang-Mills theory, and (2) the construction of topological field theory Lagrangians. Topological field theory is discussed from the point of view of infinite-dimensional differential geometry. We emphasize the unifying role of equivariant cohomology both as the underlying principle in the formulation of BRST transformation laws and as a central concept in the geometrical interpretation of topological field theory path integrals.
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Correlation functions of any number of boundary-anchored Wilson line insertions can be determined using techniques very similar to 2d Yang-Mills theory.
“Correlation functions of any number of these bilocal operator insertions can be determined using techniques very similar to 2d Yang–Mills theory (Migdal 1975; Witten 1991a; Cordes et al. 1995).”
From Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity (2023) · cites this paper as Cordes et al. 1995
Cites
Intersection theory on the moduli space of curves and the matrix airy function
Kontsevich, M. (1992) · Communications in Mathematical Physics · doi:10.1007/bf02099526 · Cited by 1,472 · see citing works
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Fermionic localization of the schwarzian theory
Stanford, D., & Witten, E. (2017) · Journal of High Energy Physics · doi:10.1007/jhep10(2017)008 · Cited by 392 · see citing works
Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity
Mertens, T. G., & Turiaci, G. J. (2023) · Living Reviews in Relativity · doi:10.1007/s41114-023-00046-1 · Cited by 181 · see citing works
Matrix ensembles with global symmetries and ’t Hooft anomalies from 2d gauge theory
Kapec, D., Mahajan, R., & Stanford, D. (2020) · Journal of High Energy Physics · doi:10.1007/jhep04(2020)186 · Cited by 45 · see citing works
- Authors
- Cordes, S., Moore, G., & Ramgoolam, S.
- Affiliations
- Yale University (US)
- Corresponding author
- Cordes, Stefan
- Moore, Gregory
- Ramgoolam, Sanjaye
- Venue
- Nuclear Physics B - Proceedings Supplements
- Publisher
- Elsevier BV
- Published
- 1995-04
- Volume
- 41
- Issue
- 1-3
- Pages
- 184-244
- ISSN
- 0920-5632 (ISSN-L)
- OpenAlex
- W2159940444
- Cited by
- 248
- References
- 1
- Citations by year
- 2026: 9 · 2025: 11 · 2024: 16 · 2023: 14 · 2022: 18 · 2021: 7 · 2020: 18 · 2019: 11 · 2018: 8 · 2017: 12 · 2016: 7 · 2015: 7 · 2014: 5 · 2013: 7 · 2012: 8
- FWCI
- 0.52
- Type
- journal article
- Language
- en
- Open access
- hybrid
- doi.org
- Licence
- Locations
- Nuclear Physics B - Proceedings Supplements (publishedVersion, cc-by-nc-nd)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
- Physical Sciences › Mathematics › Mathematical Physics › Homotopy and Cohomology in Algebraic Topology
- Physical Sciences › Mathematics › Geometry and Topology › Algebraic structures and combinatorial models
- Keywords
- two-dimensional Yang-Mills theory, equivariant cohomology, topological field theory, BRST symmetry, path integral, infinite-dimensional differential geometry
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