Effective strings in QED3

Abstract

Effective string theory describes the physics of long confining strings in theories, like Yang-Mills theory, where the mass gap \( {M}_{\textrm{gap}}^2 \) is of the same order as the string tension T. In 2 + 1 dimensions, there is a class of confining theories, including massive QED₃ as first analyzed by Polyakov, for which \( {M}_{\textrm{gap}}^2 \) ≪ T. These theories are weakly coupled at low energies of order M_gap, and may be analyzed perturbatively. In this paper, we analyze the physics of strings in such theories, focusing on QED₃, at energies of order M_gap (but still well below \( \sqrt{T} \)). We argue that the width of the string in these theories should be of order 1/M_gap independently of its length, as long as the string is not exponentially long. We also compute at leading order in perturbation theory the ground state energy of a confining string on a circle, and the scattering of Nambu-Goldstone bosons on the string worldsheet.