Imprints of asymptotic freedom on confining strings

TL;DR

This paper investigates how asymptotic freedom influences confining strings in large N Yang-Mills theory, connecting UV gauge theory behavior to flux tube dynamics and deriving bounds on scattering data of Goldstone modes.

Contribution

It establishes a link between the UV properties of gauge theories and the spectral density of string states, and derives bounds on scattering amplitudes of flux tube excitations.

Findings

Determines the asymptotic spectral density of string states.

Derives bounds on the reflection amplitude of Goldstone modes.

Rules out an asymptotically linear phase shift for the S-matrix.

Abstract

We consider the Polyakov loop correlator in the confining phase of large $N$ Yang-Mills theory in three and four dimensions. It can be computed by summing over the exchange of closed flux tubes winding around the thermal cycle. At short separations, the leading divergence is controlled by perturbation theory. Combining these two facts allows us to determine the asymptotic spectral density of string states contributing to the correlator. This sharply relates the weakly-coupled UV of the gauge theory to the dynamics of highly energetic flux tubes. Then, in a toy integrable setting, we explore how this can bound the scattering data of the Goldstone modes on top of a long string. We derive a bound on the asymptotic behavior of the reflection amplitude of Goldstones against the flux tube boundary sourced by the Polyakov line, and rule out an asymptotically linear phase shift for the S-matrix. Along the way, we discuss how causality can impose bounds on thermodynamic quantities, and show how the positivity of time delays follows from unitarity and analyticity of $2d$ massless elastic S-matrices. We include a review on reflection amplitudes, and their computation in the theory of long effective strings.