Dimensional reduction of Carroll-Field-Jackiw theory

Abstract

We investigate the dimensional reduction of the massive Carroll-Field-Jackiw (CFJ) theory from (3+1)D to (2+1)D. The resulting effective field theory, referred to as pseudo-CFJ (PCFJ), exhibits an intricate non-local structure governed by nested pseudo-differential operators. We exactly solve the static interaction potential, revealing a Coulomb-like short-distance regime and a modified Yukawa long-distance decay dictated by a topological effective mass. Finally, by applying the generalized optical theorem, we rigorously prove that the PCFJ theory violates unitarity, in stark contrast to native pseudo-quantum electrodynamics (PQED).