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arXiv · 1109.0283

4d Index to 3d Index and 2d TQFT

Francesco Benini·Tatsuma Nishioka·Masahito Yamazaki
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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).

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Francesco Benini, Tatsuma Nishioka, Masahito Yamazaki. 2012-08-12. 4d Index to 3d Index and 2d TQFT. https://doi.org/10.1103/physrevd.86.065015

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