Analytic continuation of dimensions in supersymmetric localization

Gorantis, Anastasios; Minahan, Joseph A.; Naseer, Usman

doi:10.1007/jhep02(2018)070

Title: Analytic continuation of dimensions in supersymmetric localization

Journal Article · Mon Feb 12 00:00:00 EST 2018 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep02(2018)070· OSTI ID:1498698

Gorantis, Anastasios ^[1]; Minahan, Joseph A. ^[1]; Naseer, Usman ^[2]

Uppsala Univ. (Sweden). Dept. of Physics and Astronomy
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Center for Theoretical Physics

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* 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.

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Research Organization:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: SC0012567

OSTI ID:: 1498698

Journal Information:: Journal of High Energy Physics (Online), Vol. 2018, Issue 2; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 11 works

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References (33)

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Gauge theories on spheres with 16 supercharges and non-constant couplings Minahan, Joseph A.; Naseer, Usman Journal of Physics A: Mathematical and Theoretical, Vol. 52, Issue 23 https://doi.org/10.1088/1751-8121/ab1ab1	journal	May 2019
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Partition Functions of $\mathcal{N}=1$ Gauge Theories on $S^2 \times \mathbb{R}^2_\varepsilon$ and Duality Kimura, Taro; Nian, Jun; Zhao, Peng arXiv https://doi.org/10.48550/arxiv.1812.11188	text	January 2018

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