Confining String with Topological Term

TL;DR

This paper explores the properties of confining strings in gauge theories, deriving their effective actions, analyzing the impact of a topological theta-term, and confirming the negative stiffness coefficient through duality and semiclassical methods.

Contribution

It provides an exact duality transformation to derive the confining string action, incorporates a theta-term in 4D, and analyzes the resulting effective string actions including stability considerations.

Findings

The confining string action reduces to the Polyakov action semiclassically.

The negative extrinsic curvature coefficient confirms previous proposals.

The theta-term allows for renormalization and stabilization of the string system.

Abstract

We consider several aspects of `confining strings', recently proposed to describe the confining phase of gauge field theories. We perform the exact duality transformation that leads to the confining string action and show that it reduces to the Polyakov action in the semiclassical approximation. In 4D we introduce a `$\theta$-term' and compute the low-energy effective action for the confining string in a derivative expansion. We find that the coefficient of the extrinsic curvature (stiffness) is negative, confirming previous proposals. In the absence of a $\theta$-term, the effective string action is only a cut-off theory for finite values of the coupling e, whereas for generic values of $\theta$, the action can be renormalized and to leading order we obtain the Nambu-Goto action plus a topological `spin' term that could stabilize the system.