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arXiv · 2412.02514

A Nonlocal Schwinger Model

Ludovic Fraser-Taliente·Christopher P. Herzog·Abhay Shrestha
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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.

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Ludovic Fraser-Taliente, Christopher P. Herzog, Abhay Shrestha. 2024-12-03. A Nonlocal Schwinger Model. https://arxiv.org/abs/2412.02514

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