4d Index to 3d Index and 2d TQFT

Details 4d Index to 3d Index and 2d TQFT 4d Index to 3d Index and 2d TQFT

2011-09-01

arxiv.org/abs/1109.0283v1

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, 2 figures

Scientific paper

We compute the 4d superconformal index for N=1, 2 gauge theories on S^1 x L(p,q), where L(p,q) 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 the 4d index on S^1 x L(p,q) to a 3d partition function on a squashed L(p,q) 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 (2,0) theory on a punctured Riemann surface, and conjecture the existence of a 2d TQFT on the Riemann surface whose correlation function coincides with the 4d N =2 index on S^1 x L(p,q).

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