The arithmetic of supersymmetric vacua

Antoine Bourget; Jan Troost

doi:10.1007/JHEP07(2016)036

The arithmetic of supersymmetric vacua

Antoine Bourget
, Jan Troost

Université PSL

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

Abstract: We provide explicit formulas for the number of vacua of four-dimensional pure N = 1 super Yang-Mills theories on a circle, with any simple gauge algebra and any choice of center and spectrum of line operators. The formula for the (SU(N)/ℤm)n theory is a key ingredient in the semi-classical calculation of the number of massive vacua of N = 1^∗ gauge theories with gauge algebra su(n) , compactified on a circle. Using arithmetic, we express that number in an S L (2 ℤ) duality invariant manner. We confirm our tally of massive vacua of the N = 1^∗ theories by a count of inequivalent extrema of the exact superpotential.

Original language	English
Article number	36
Journal	Journal of High Energy Physics
Volume	2016
Issue number	7
DOIs	https://doi.org/10.1007/JHEP07(2016)036
Publication status	Published - 1 Jul 2016
Externally published	Yes

Keywords

Duality in Gauge Field Theories
Supersymmetric gauge theory
Wilson
’t Hooft and Polyakov loops

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10.1007/JHEP07(2016)036

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title = "The arithmetic of supersymmetric vacua",

abstract = "Abstract: We provide explicit formulas for the number of vacua of four-dimensional pure N = 1 super Yang-Mills theories on a circle, with any simple gauge algebra and any choice of center and spectrum of line operators. The formula for the (SU(N)/ℤm)n theory is a key ingredient in the semi-classical calculation of the number of massive vacua of N = 1∗ gauge theories with gauge algebra su(n) , compactified on a circle. Using arithmetic, we express that number in an S L (2 ℤ) duality invariant manner. We confirm our tally of massive vacua of the N = 1∗ theories by a count of inequivalent extrema of the exact superpotential.",

keywords = "Duality in Gauge Field Theories, Supersymmetric gauge theory, Wilson, {\textquoteright}t Hooft and Polyakov loops",

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N2 - Abstract: We provide explicit formulas for the number of vacua of four-dimensional pure N = 1 super Yang-Mills theories on a circle, with any simple gauge algebra and any choice of center and spectrum of line operators. The formula for the (SU(N)/ℤm)n theory is a key ingredient in the semi-classical calculation of the number of massive vacua of N = 1∗ gauge theories with gauge algebra su(n) , compactified on a circle. Using arithmetic, we express that number in an S L (2 ℤ) duality invariant manner. We confirm our tally of massive vacua of the N = 1∗ theories by a count of inequivalent extrema of the exact superpotential.

AB - Abstract: We provide explicit formulas for the number of vacua of four-dimensional pure N = 1 super Yang-Mills theories on a circle, with any simple gauge algebra and any choice of center and spectrum of line operators. The formula for the (SU(N)/ℤm)n theory is a key ingredient in the semi-classical calculation of the number of massive vacua of N = 1∗ gauge theories with gauge algebra su(n) , compactified on a circle. Using arithmetic, we express that number in an S L (2 ℤ) duality invariant manner. We confirm our tally of massive vacua of the N = 1∗ theories by a count of inequivalent extrema of the exact superpotential.

KW - Duality in Gauge Field Theories

KW - Supersymmetric gauge theory

KW - Wilson

KW - ’t Hooft and Polyakov loops

UR - https://www.scopus.com/pages/publications/84978063166

U2 - 10.1007/JHEP07(2016)036

DO - 10.1007/JHEP07(2016)036

M3 - Article

AN - SCOPUS:84978063166

SN - 1126-6708

VL - 2016

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 7

M1 - 36

ER -

The arithmetic of supersymmetric vacua

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Keywords

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