4d Index to 3d Index and 2d TQFT
High Energy Physics - Theory
2012-09-17 v2
Abstract
We compute the 4d superconformal index for N=1,2 gauge theories on S^1 x L(p,1), where L(p,1) is a lens space. We find that the 4d N=1,2 index on S^1 x L(p,1) reduces to a 3d N=2,4 index on S^1 x S^2 in the large p limit, and to a 3d partition function on a squashed L(p,1) when the size of temporal S^1 shrinks to zero. As an application of our index, we study 4d N=2 superconformal field theories arising from the 6d N=(2,0) A_1 theory on a punctured Riemann surface, and conjecture the existence of a 2d Topological Quantum Field Theory on the Riemann surface whose correlation function coincides with the 4d N=2 index on S^1 x L(p,1).
Keywords
Cite
@article{arxiv.1109.0283,
title = {4d Index to 3d Index and 2d TQFT},
author = {Francesco Benini and Tatsuma Nishioka and Masahito Yamazaki},
journal= {arXiv preprint arXiv:1109.0283},
year = {2012}
}
Comments
24 pages, 2 figures; v2: typos corrected, refs added, discussion of L(p,q) removed