Form factor and width of a quantum string

TL;DR

This paper investigates the logarithmic broadening of confining strings in quantum field theories using the string form factor, measured via lattice simulations in the 3D Ising model and related theories.

Contribution

It introduces a method to extract the string form factor from correlation functions and demonstrates its logarithmic broadening in a strongly coupled scalar theory.

Findings

String form factor exhibits logarithmic broadening.

Method applicable to lattice Monte Carlo simulations.

Results consistent with previous observations of string broadening.

Abstract

In the Yang-Mills theory, the apparent thickness of the confining string is known to grow logarithmically when its length increases. The same logarithmic broadening also happens to strings in other quantum field theories and domain walls in statistical physics models. Even in quantum field theories, the correlators used to measure and characterise this phenomenon are analogous to those in statistical physics. In this paper we describe it using the string form factor which is a meaningful quantum observable, obtainable in principle from scattering experiments. We show how the form factor can be obtained from field correlation functions calculated in lattice Monte Carlo simulations. We apply this method to 2+1-dimensional scalar theory in the strong coupling limit, where it is equivalent to the 3D Ising model, and through duality also to 2+1-dimensional $\mathbb{Z}_2$ gauge theory. We measure the string form factor by simulating the Ising model, and demonstrate that it displays the same logarithmic broadening as observed by other quantities.