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arXiv · 1512.06924

Localizing gauge theories on $S^d$

Joseph A. Minahan
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Abstract

We conjecture the form of the one-loop determinants for localized gauge theories with eight supersymmetries on $d$-dimensional spheres. Combining this with results for the localized action, we investigate the strong coupling behavior in the large $N$ limit for a continuous range of $d$. In particular, we find the $N$ dependence of the free energy for supersymmetric Yang-Mills with only a vector multiplet in $3<d<4$ and for maximally supersymmetric Yang-Mills in $3< d<6$. We also argue that this gives an effective way to regularize divergences after localization in $d=4$ for ${\mathcal N}=2$ gauge theories and $d=6$ for the maximally supersymmetric case.

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Joseph A. Minahan. 2016-04-29. Localizing gauge theories on $S^d$. https://doi.org/10.1007/jhep04(2016)152

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