Hunting 3d N $$ \mathcal{N} $$ = 1 SQED in the ϵ-expansion

Abstract

Abstract It was recently shown that 3d N $$ \mathcal{N} $$ = 1 supersymmetric Wess-Zumino models can be studied in the ϵ-expansion by analytically continuing the number of fermionic degrees of freedom to be half-integer. In this work we study the extension of this strategy to gauge theories. We consider U(1) gauge theories with N g neutral Majorana fermions χ a , N f charge-1 bosons ϕ i and N f × N g charge-1 Dirac fermions ψ ia in the d = 4 − 2ϵ expansion. Analytically continuing to N g = 1 2 $$ \frac{1}{2} $$ schematically matches the Lagrangian and matter content of 3d N $$ \mathcal{N} $$ = 1 SQED, and we check whether this match can be made rigorous. We compute anomalous dimensions of χ a up to two loops and of meson operators up to one loop at the fixed points, and compare to expectations from SUSY. While we find obstructions to SUSY at small N f , at large N f the observables approach the expected values at a SUSY fixed point. This may allow for checks of 3d N $$ \mathcal{N} $$ = 1 IR dualities between gauge theories.

Keywords

• Field Theories in Lower Dimensions
• Renormalization Group
• Scale and Conformal Symmetries
• Supersymmetry and Duality