Superconformal Index and 3d-3d Correspondence for Mapping Cylinder/Torus
arXiv:1305.0937 · doi:10.1007/JHEP01(2014)063
Abstract
We probe the 3d-3d correspondence for mapping cylinder/torus using the superconformal index. We focus on the case when the fiber is a once-punctured torus (Σ_{1,1}). The corresponding 3d field theories can be realized using duality domain wall theories in 4d N=2* theory. We show that the superconformal indices of the 3d theories are the SL(2,C) Chern-Simons partition function on the mapping cylinder/torus. For the mapping torus, we also consider another realization of the corresponding 3d theory associated with ideal triangulation. The equality between the indices from the two descriptions for the mapping torus theory is reduced to a basis change of the Hilbert space for the SL(2,C) Chern-Simons theory on RxΣ_{1,1}.
66 pages, 6 figures. v2: references added. v3:Minor corrections, refs added
References in corpus (10)
- The 4d Superconformal Index from q-deformed 2d Yang-Mills
- Generalized Superconformal Index for Three Dimensional Field Theories
- On Three Dimensional Quiver Gauge Theories and Integrability
- Superconformal indices of three-dimensional theories related by mirror symmetry
- AGT on the S-duality Wall
- 3d TQFT from 6d SCFT
- Superconformal Index with Duality Domain Wall
- Chern-Simons Theory and S-duality
- Complex Chern-Simons from M5-branes on the Squashed Three-Sphere
- Ground States of S-duality Twisted N=4 Super Yang-Mills Theory
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