Loop operators and S-duality from curves on Riemann surfaces

2009/07/15 by Nadav Drukker, David R. Morrison, David R Morrison +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Dirac (video compression format) #Duality (order theory) #Gauge (firearms) #Gauge group #Gauge theory #Homotopy #Homotopy and Cohomology in Algebraic Topology #Loop (graph theory) #Product (mathematics) #Quantization (signal processing) #Riemann surface #hep-th #math.GT

paper · pdf · doi:10.1088/1126-6708/2009/09/031

published as JHEP 0909:031,2009 · 41 pages

arxiv created 2009/07/15 · openalex publication_date 2009/09/03 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We study Wilson-'t Hooft loop operators in a class of N=2 superconformal field theories recently introduced by Gaiotto. In the case that the gauge group is a product of SU(2) groups, we classify all possible loop operators in terms of their electric and magnetic charges subject to the Dirac quantization condition. We then show that this precisely matches Dehn's classification of homotopy classes of non-self-intersecting curves on an associated Riemann surface--the same surface which characterizes the gauge theory. Our analysis provides an explicit prediction for the action of S-duality on loop operators in these theories which we check against the known duality transformation in several examples.

Citations

• An exact prediction of N=4 supersymmetric Yang–Mills theory for string theory
• A presentation for the mapping class group of a closed orientable surface
• On the phase transition towards permanent quark confinement
• A finite set of generators for the homeotopy group of a 2-manifold

Cited by

• Analysis of correlation functions in Toda theory and the Alday-Gaiotto-Tachikawa-Wyllard relation forSU(3)quiver
• The toroidal block and the genus expansion