Analytic continuation of dimensions in supersymmetric localization
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Author(s)
Gorantis, Anastasios
Minahan, Joseph A.
Naseer, Usman
Date Issued
February 2018
Journal
Journal of High Energy Physics
Publisher
Springer Berlin Heidelberg
Citation
Gorantis, Anastasios, et al. “Analytic Continuation of Dimensions in Supersymmetric Localization.” Journal of High Energy Physics, vol. 2018, no. 2, Feb. 2018. © The Authors
Version
Final published version
Abstract
We compute the perturbative partition functions for gauge theories with eight supersymmetries on spheres of dimension d ≤ 5, proving a conjecture by the second author. We apply similar methods to gauge theories with four supersymmetries on spheres with d ≤ 3. The results are valid for non-integer d as well. We further propose an analytic continuation from d = 3 to d = 4 that gives the perturbative partition function for an N =1 gauge theory. The results are consistent with the free multiplets and the one-loop β-functions for general N = 1 gauge theories. We also consider the analytic continuation of an N = 1 preserving mass deformation of the maximally supersymmetric gauge theory and compare to recent holographic results for N = 1[superscript ∗] super Yang-Mills. We find that the general structure for the real part of the free energy coming from the analytic continuation is consistent with the holographic results. Keywords: Extended Supersymmetry, Matrix Models, Supersymmetric Gauge Theory
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Department of Physics
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DOI of Published Version
https://doi.org/10.1007/JHEP02(2018)070
