Localizing gauge theories on $S^d$

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.

17 pages; v2: Typos corrected

References in corpus (2)

• Bootstrapping SCFTs with Four Supercharges
• Quantum Electrodynamics in d=3 from the epsilon-expansion

Cited by in corpus (12)

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• The F-Theorem and F-Maximization
• Introduction to localization in quantum field theory
• Analytic continuation of dimensions in supersymmetric localization
• One-loop tests of supersymmetric gauge theories on spheres
• 7D supersymmetric Yang-Mills on curved manifolds
• Phases of five-dimensional supersymmetric gauge theories
• Linear Quivers at Large-$N$
• Deconstructing Little Strings with $\mathcal{N}=1$ Gauge Theories on Ellipsoids
• (1,0) gauge theories on the six-sphere
• Wilson Loops and Spherical Branes
• Gauge theories on spheres with 16 supercharges and non-constant couplings