A nonlocal Schwinger model
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 Fϕ-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.