A Nonlocal Schwinger Model

TL;DR

This paper analyzes a generalized nonlocal Schwinger model in various dimensions, revealing how the scalar field's behavior transitions from free in the ultraviolet to nontrivial in the infrared, with implications for Maxwell theory defects.

Contribution

It extends the Schwinger model to higher dimensions, showing the scalar's renormalization group flow and the triviality of conformal defects in Maxwell theory at four dimensions.

Findings

In 2D, the photon acquires a mass as in the classic Schwinger model.

In 2<d<4, the scalar exhibits a nontrivial RG flow from free to interacting.

At d=4, the defect becomes trivial in the IR limit.

Abstract

We solve a system of massless fermions constrained to two space-time dimensions interacting via a $d$ space-time dimensional Maxwell field. Through dimensional reduction to the defect and bosonization, the system maps to a massless scalar interacting with a nonlocal Maxwell field through a $F \phi$-coupling. The $d=2$ dimensional case is the usual Schwinger model where the photon gets a mass. More generally, in $2<d<4$ dimensions, the degrees of freedom map to a scalar which undergoes a renormalization group flow; in the ultraviolet, the scalar is free, while in the infrared it has scaling dimension $(4-d)/2$. The infrared is similar to the Wilson-Fisher fixed point, and the physically relevant case $d=4$ becomes infrared trivial in the limit of infinite ultraviolet cut-off, consistent with earlier work on the triviality of conformal surface defects in Maxwell theory.