Closed k-strings in SU(N) gauge theories : 2+1 dimensions

TL;DR

This study computes the energies of closed k-strings in (2+1)-dimensional SU(N) gauge theories, showing they align with an effective bosonic string model and revealing detailed N-dependence and representation-specific spectra.

Contribution

It provides the first detailed calculations of k-string energies in (2+1)D SU(N) theories for multiple N and k values, confirming effective string descriptions and representation effects.

Findings

k-strings follow Nambu-Goto universality class

String tension ratios are close to Casimir scaling, slightly above it

Spectrum sectors correspond to specific SU(N) irreducible representations

Abstract

We calculate the ground state energies of closed k-strings in (2+1)-dimensional SU(N) gauge theories, for N=4,5,6,8 and k=2,3,4. From the dependence of the ground state energy on the string length, we infer that such k-strings are described by an effective string theory that is in the same bosonic universality class (Nambu-Goto) as the fundamental string. When we compare the continuum k-string tensions to the corresponding fundamental string tensions, we find that the ratios are close to, but typically 1-2 percent above, the Casimir scaling values favoured by some theoretical approaches. Fitting the N-dependence in a model-independent way favours an expansion in 1/N (as in Casimir scaling) rather than the 1/N^2 that is suggested by naive colour counting. We also observe that the low-lying spectrum of k-string states falls into sectors that belong to particular irreducible representations of SU(N), demonstrating that the dynamics of string binding knows about the full gauge group and not just about its centre.