Beta-functions for a SU(2) Matrix Model in 2 + epsilon Dimensions

Abstract

To investigate the non-perturbative, electric sector of a deconfined gauge theory at nonzero temperature, we consider a SU(2) matrix model. We compute beta-functions to one loop order for the simplest extension of the O(4) nonlinear sigma model, which involves three coupling constants. Computing in the ultraviolet limit in 2 + epsilon dimensions, we find that at least one coupling is not asymptotically free.

Published version; added discussion of hep-ph/0608242

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• Hard thermal loops, to quadratic order, in the background of a spatial 't Hooft loop
• Collisional energy loss above the critical temperature in QCD
• Gross-Witten-Wadia transition in a matrix model of deconfinement
• Finite-temperature phase transitions of third and higher order in gauge theories at large $N$
• Free energy of a Holonomous Plasma
• Effective models of a semi-quark gluon plasma
• Matrix model for deconfinement in an SU(2) gauge theory in 2+1 dimensions
• Matrix model for deconfinement in a SU(Nc) gauge theory in 2+1 dimensions
• Wilson loops in the Hamiltonian formalism
• Shear and bulk viscosity for a pure glue theory using an effective matrix model