<p>We solve a system of massless fermions constrained to two space-time dimensions interacting via a <i>d</i> 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 <i>Fϕ</i>-coupling. The <i>d</i> = 2 dimensional case is the usual Schwinger model where the photon gets a mass. More generally, in 2 &lt; <i>d</i> &lt; 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 – <i>d</i>)/2. The infrared is similar to the Wilson-Fisher fixed point, and the physically relevant case <i>d</i> = 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.</p>

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A nonlocal Schwinger model

  • Ludo Fraser-Taliente,
  • Christopher P. Herzog,
  • Abhay Shrestha

摘要

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 -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.