Poincare invariance in effective string theories

TL;DR

This paper studies the relativistic dispersion relations of closed-string states in SU(N) gauge theories using effective string theories, providing explicit calculations up to two-loop order and exploring generalizations to transverse compact dimensions.

Contribution

It demonstrates that energy eigenstates satisfy relativistic dispersion relations order by order and explicitly computes matrix elements in the Luscher-Weisz effective string theory up to two loops.

Findings

Energy eigenstates obey relativistic dispersion relations order by order.

Explicit two-loop calculations of Polyakov loop matrix elements.

Potential generalization to transverse compact dimensions.

Abstract

We investigate the dispersion relation of the winding closed-string states in SU(N) gauge theory defined on a d-dimensional hypertorus, in a class of effective string theories. We show that order by order in the asymptotic expansion, each energy eigenstate satisfies a relativistic dispersion relation. This is illustrated in the Luscher-Weisz effective string theory to two-loop order, where the Polyakov loop matrix elements between the vacuum and the closed string states are obtained explicitly. We attempt a generalization of these considerations to the case of compact dimensions transverse to the string.