A different kind of string

TL;DR

This study investigates the effective string describing flux tubes in 3D U(1) lattice gauge theory, revealing deviations from Nambu-Goto behavior and evidence for an extrinsic curvature term predicted by Polyakov, with implications for broader gauge theories.

Contribution

The paper provides the first numerical evidence for an extrinsic curvature term in the effective string action of a confining gauge theory, confirming Polyakov's theoretical prediction.

Findings

Deviations from Nambu-Goto string behavior observed.

Evidence for extrinsic curvature term in the effective string.

The extrinsic curvature term dominates in the continuum limit.

Abstract

In U(1) lattice gauge theory in three spacetime dimensions, the problem of confinement can be studied analytically in a semi-classical approach, in terms of a gas of monopoles with Coulomb-like interactions. In addition, this theory can be mapped to a spin model via an exact duality transformation, which allows one to perform high-precision numerical studies of the confining potential. Taking advantage of these properties, we carried out an accurate investigation of the effective string describing the low-energy properties of flux tubes in this confining gauge theory. We found striking deviations from the expected Nambu-Goto-like behavior, and, for the first time, evidence for contributions that can be described by a term proportional to the extrinsic curvature of the effective string worldsheet. Such term is allowed by Lorentz invariance, and its presence in the infrared regime of the U(1) model was indeed predicted by Polyakov several years ago. Our results show that this term scales as expected according to Polyakov's solution, and becomes the dominant contribution to the effective string action in the continuum limit. We also demonstrate analytically that the corrections to the confining potential induced by the extrinsic curvature term can be related to the partition function of the massive perturbation of a c=1 bosonic conformal field theory. The implications of our results for SU(N) Yang-Mills theories in three and in four spacetime dimensions are discussed.