A different kind of string

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 highprecision 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.

T T ¯ $$ \mathrm{T}\overline{\mathrm{T}} $$ -deformed 2D quantum field theories

“…Particularly interesting is the idea that also massive excitations could propagate on the flux-tube. It would be wonderful if TCSA could help to find a precise perturbed CFT interpretation of the pseudoscalar particle whose presence on the 4D QCD flux tube was recently conjectured on the basis of numerical data and TBA-inspired computations [7], or the massive mode discovered through Monte Carlo simulations in the 3D U(1) gauge-theory [56].…”

On the spectrum and string tension of U(1) lattice gauge theory in 2 + 1 dimensions

“…That is one of the aims of this paper. Another aim is to calculate the spectrum of non-contractible closed flux tubes that wind around one of the periodic spatial directions, so as to learn what we can about the effective world-sheet action of such flux tubes in the U(1) gauge theory, thus complementing recent studies [12,13] of the ground state of a flux tube between static sources.…”

Flux tubes in the QCD vacuum

“…As a matter of fact, a careful study, within the dual superconductor model, of the dependence of the flux tube shape on the distance between the color sources has not been carried out so far either at zero temperature, at least in non-Abelian lattice field theories. In the threedimensional Abelian U(1) lattice gauge theory, instead, such an analysis has been completed very recently [43].…”