Localization of the four-dimensional N=4 SYM to a two-sphere and 1/8 BPS Wilson loops

2009/06/30 by Vasily Pestun · 5 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Conjecture #Instanton #Loop (graph theory) #M-theory #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #String theory #Supersymmetry #Wilson loop #hep-th

paper · pdf · doi:10.1007/jhep12(2012)067

49 pages; v3: typos corrected

arxiv created 2012/09/20 · openalex publication_date 2012/12/01 · arxiv updated 2015/05/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We localize the four-dimensional N=4 super Yang-Mills theory on a four-sphere to the two-dimensional constrained Hitchin/Higgs-Yang-Mills (cHYM) theory on a two-sphere S². We show that expectation values of certain 1/8 BPS supersymmetric Wilson loops on S² in the 4d N=4 SYM is captured by the 2d cHYM theory. We further argue that expectation values of Wilson loops in the cHYM theory agree with the prescription "two-dimensional bosonic Yang-Mills excluding instanton contributions". Hence, we support the recent conjecture by Drukker, Giombi, Ricci and Trancanelli on the 1/8 BPS Wilson loops on S² in the 4d N=4 SYM.

Citations

• The Self-Duality Equations on a Riemann Surface
• An exact prediction of N=4 supersymmetric Yang–Mills theory for string theory
• Electric-magnetic duality and the geometric Langlands program
• Two Dimensional Gauge Theories Revisited
• The moment map and equivariant cohomology
• Topological quantum field theory
• The large N limit of superconformal field theories and supergravity

Cited by

• The topological line of ABJ(M) theory
• String corrections to circular Wilson loop and anomalies
• Exact Bremsstrahlung functions in ABJM theory
• Exact correlators on the Wilson loop in N=4 SYM: localization, defect CFT, and integrability
• Wilson loop correlators in N = 2 superconformal quivers