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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.
In our recent work [Phys. Rev. Lett. 102, 230502 (2009)] we showed that the partition function of all classical spin models, including all discrete standard statistical models and all Abelian discrete lattice gauge theories (LGTs), can be expressed a
We investigate the quantum entanglement entropy for the four-dimensional Euclidean SU(3) gauge theory. We present the first non-perturbative calculation of the entropic $c$-function ($C(l)$) of SU(3) gauge theory in lattice Monte Carlo simulation usi
We apply Gauge Theory of Arbitrage (GTA) {hep-th/9710148} to derivative pricing. We show how the standard results of Black-Scholes analysis appear from GTA and derive correction to the Black-Scholes equation due to a virtual arbitrage and speculators
We study the +/- J random-plaquette Z_2 gauge model (RPGM) in three spatial dimensions, a three-dimensional analog of the two-dimensional +/- J random-bond Ising model (RBIM). The model is a pure Z_2 gauge theory in which randomly chosen plaquettes (
We show that the partition function of all classical spin models, including all discrete Standard Statistical Models and all abelian discrete Lattice Gauge Theories (LGTs), can be expressed as a special instance of the partition function of the 4D Z_