Abstract
We provide explicit formulas for the number of vacua of four-dimensional pure \( \mathcal{N} \) = 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 \( {\left(\mathrm{S}\mathrm{U}(N)/{\mathbb{Z}}_m\right)}_n \) theory is a key ingredient in the semi-classical calculation of the number of massive vacua of \( \mathcal{N} \) = 1∗ gauge theories with gauge algebra \( \mathfrak{s}\mathfrak{u}(n) \), compactified on a circle. Using arithmetic, we express that number in an \( \mathrm{S}\mathrm{L}\left(2,\mathbb{Z}\right) \) duality invariant manner. We confirm our tally of massive vacua of the \( \mathcal{N} \) = 1∗ theories by a count of inequivalent extrema of the exact superpotential.
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ArXiv ePrint: 1606.01022
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Bourget, A., Troost, J. The arithmetic of supersymmetric vacua. J. High Energ. Phys. 2016, 36 (2016). https://doi.org/10.1007/JHEP07(2016)036
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DOI: https://doi.org/10.1007/JHEP07(2016)036