Confinement in large N gauge theories

TL;DR

This paper investigates volume reduction in large N gauge theories, showing that twisted Eguchi-Kawai models match finite N results for string tension and exploring different behaviors for theories with 1 or 2 adjoint quark flavors.

Contribution

It provides evidence supporting volume reduction in large N gauge theories and explores the effects of adjoint quark flavors on string tension and infrared fixed points.

Findings

String tension matches between twisted Eguchi-Kawai model and finite N extrapolations.

Finite string tension for 1 flavor at the massless limit.

String tension vanishes with a large anomalous dimension for 2 flavors.

Abstract

We report some recent results obtained for large N gauge theories which support the idea of volume reduction. Results for the string tension of the Twisted Eguchi-Kawai model match with those obtained from extrapolation from finite N. Determination of other observables is currently under way. Application of the twisted reduction idea to the case of 1 or 2 flavours of quarks in the adjoint representation of the group offers promising results. Preliminary results for the string tension point towards a very different behaviour for 1 and 2 flavours. While the string tension remains finite for 1 flavour at the critical massless quark limit, it seems to vanish with a large anomalous dimension for the $N_f=2$ case. This is consistent with the predicted Infrared fixed point expected in the latter case.