A solvable twisted one-plaquette model

TL;DR

This paper analytically solves a twisted Eguchi-Kawai model in the deconfined phase, revealing eigenvalue distributions and phase transition behavior related to classical solution condensation and phase transitions in QCD2.

Contribution

It provides an exact solution for the eigenvalue distribution and phase structure of a twisted one-plaquette model, highlighting novel features like eigenvalue bunching and phase instability.

Findings

Eigenvalues form L bunches with semicircular distribution

Model becomes unstable at a critical coupling value

Reproduces coupling dependence consistent with previous results

Abstract

We solve a hot twisted Eguchi-Kawai model with only timelike plaquettes in the deconfined phase, by computing the quadratic quantum fluctuations around the classical vacuum. The solution of the model has some novel features: the eigenvalues of the time-like link variable are separated in L bunches, if L is the number of links of the original lattice in the time direction, and each bunch obeys a Wigner semicircular distribution of eigenvalues. This solution becomes unstable at a critical value of the coupling constant, where it is argued that a condensation of classical solutions takes place. This can be inferred by comparison with the heat-kernel model in the hamiltonian limit, and the related Douglas-Kazakov phase transition in QCD2. As a byproduct of our solution, we can reproduce the dependence of the coupling constant from the parameter describing the asymmetry of the lattice, in agreement with previous results by Karsch.