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arXiv · 2012.15857

A Large-$N$ Phase Transition in a Finite Lattice Gauge Theory

Nirmalya Brahma·Chethan Krishnan
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Abstract

We consider gauge theories of non-Abelian $finite$ groups, and discuss the 1+1 dimensional lattice gauge theory of the permutation group $S_N$ as an illustrative example. The partition function at finite $N$ can be written explicitly in a compact form using properties of $S_N$ conjugacy classes. A natural large-$N$ limit exists with a new 't Hooft coupling, $\lambda=g^2 \log N$. We identify a Gross-Witten-Wadia-like phase transition at infinite $N$, at $\lambda=2$. It is first order. An analogue of the string tension can be computed from the Wilson loop expectation value, and it jumps from zero to a finite value. We view this as a type of large-$N$ (de-)confinement transition. Our holographic motivations for considering such theories are briefly discussed.

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hep-thcond-mat.stat-mechhep-lat

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BibTeXRIS

Nirmalya Brahma, Chethan Krishnan. 2020-12-31. A Large-$N$ Phase Transition in a Finite Lattice Gauge Theory. https://doi.org/10.1103/physrevd.103.126028

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