Large N and confining flux tubes as strings - a view from the lattice

TL;DR

This paper reviews lattice simulation insights into large-N gauge theories, confirming confinement and the relevance of Nambu-Goto string theory for describing flux tubes, with recent progress extending effective string descriptions.

Contribution

It provides new lattice results and analytic progress supporting Nambu-Goto string theory as the effective description of confining flux tubes in SU(N) gauge theories.

Findings

SU(3) closely approximates SU(∞) for many quantities

Lattice calculations support Nambu-Goto string as effective model

Extended Luscher correction terms improve string spectrum predictions

Abstract

I begin these three lectures by describing some of the useful things that we have learned about large-N gauge theories using lattice simulations. For example that the theory is confining in that limit, that for many quantities SU(3) is close to SU(oo), and that this includes the strongly coupled gluon plasma just above Tc, thus providing some of the justification needed to make use of gauge-gravity duality in analysing QCD at RHIC/LHC temperatures. I then turn, in a more detailed discussion, to recent progress on the problem of what effective string theory describes confining flux tubes. I describe lattice calculations of the energy spectrum of closed loops of confining flux, and some dramatic analytic progress in extending the `universal Luscher correction' to terms that are of higher order in 1/l, where l is the length of the string. Both approaches point increasingly to the Nambu-Goto free string theory as being the appropriate starting point for describing string-like degrees of freedom in SU(N) gauge theories.