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arXiv · 1104.4470

Localization of N=4 Superconformal Field Theory on S^1 x S^3 and Index

Satoshi Nawata
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Abstract

We provide the geometrical meaning of the ${\cal N}=4$ superconformal index. With this interpretation, the ${\cal N}=4$ superconformal index can be realized as the partition function on a Scherk-Schwarz deformed background. We apply the localization method in TQFT to compute the deformed partition function since the deformed action can be written as a $δ_ε$-exact form. The critical points of the deformed action turn out to be the space of flat connections which are, in fact, zero modes of the gauge field. The one-loop evaluation over the space of flat connections reduces to the matrix integral by which the ${\cal N}=4$ superconformal index is expressed.

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Satoshi Nawata. 2011-11-23. Localization of N=4 Superconformal Field Theory on S^1 x S^3 and Index. https://doi.org/10.1007/jhep11(2011)144

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