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arXiv · 1801.05460

Holonomy Saddles and Supersymmetry

Chiung Hwang·Sungjay Lee·Piljin Yi
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Abstract

In gauge theories on a spacetime equipped with a circle, the holonomy variables, living in the Cartan torus, play special roles. With their periodic nature properly taken into account, we find that a supersymmetric gauge theory in $d$ dimensions tends to reduce in the small radius limit to a disjoint sum of multiple $(d-1)$ dimensional theories at distinct holonomies, called $H$-saddles. The phenomenon occurs regardless of the spacetime dimensions, and here we explore such $H$-saddles for $d=4$ $\cal N=1$ theories on $T^2$ fibred over $\Sigma_g$, in the limits of elongated $T^2$. This naturally generates novel relationships between 4d and 3d partition functions, including ones between 4d and 3d Witten indices, and also leads us to re-examine recent studies of the Cardy exponents and the Casimir energies and of their purported connections to the 4d anomalies.

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Chiung Hwang, Sungjay Lee, Piljin Yi. 2018-01-16. Holonomy Saddles and Supersymmetry. https://doi.org/10.1103/physrevd.97.125013

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