SL(2,R) Chern-Simons, Liouville, and Gauge Theory on Duality Walls
Mar, 2011Citations per year
Abstract: (arXiv)
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 S^3, which is realized as a duality domain wall in a 4d gauge theory on S^4. 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.Note:
- 53+1 pages, 14 figures/ v2: typos corrected, references added
- Supersymmetry and Duality
- Field Theories in Lower Dimensions
- Chern-Simons Theories
- Matrix Models
- field theory: Liouville
- field theory: conformal
- gauge field theory: SL(2,R)
- partition function
- Chern-Simons term
- duality
References(107)
Figures(15)