2011/03/31 by Yuji Terashima, Masahito Yamazaki · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Duality (order theory) #Equivalence (formal languages) #Gauge theory #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Partition function (quantum field theory) #Quantum field theory #Riemann surface #S-duality #Seiberg duality #Supersymmetric gauge theory #Topological quantum field theory #hep-th #math.QA
paper · pdf · doi:10.1007/jhep08(2011)135
published as JHEP 1108:135,2011 · 53+1 pages, 14 figures; v2: typos corrected, references added
arxiv created 2011/07/20 · openalex publication_date 2011/08/01 · arxiv updated 2011/09/05 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We propose an equivalence of the partition functions of two different 3d gauge theories. On one side of the correspondence we consider the partition function of 3d SL(2,R) Chern-Simons theory on a 3-manifold, obtained as a punctured Riemann surface times an interval. On the other side we have a partition function of a 3d N=2 superconformal field theory on S3, which is realized as a duality domain wall in a 4d gauge theory on S4. We sketch the proof of this conjecture using connections with quantum Liouville theory and quantum Teichmuller theory, and study in detail the example of the once-punctured torus. Motivated by these results we advocate a direct Chern-Simons interpretation of the ingredients of (a generalization of) the Alday-Gaiotto-Tachikawa relation. We also comment on M5-brane realizations as well as on possible generalizations of our proposals.