Probing bad theories with the dualization algorithm. Part I

Abstract

Abstract Recently an algorithm to build SL(2, ℤ) duals, including mirror duals, of 3d N $$ \mathcal{N} $$ = 4 quiver theories and their 4d N $$ \mathcal{N} $$ = 1 uplift has been introduced. In this work we use this new tool to study the so-called bad theories. Our approach allows us to determine exactly indices/partition functions for generic values of fugacities/real mass and FI parameters revealing their surprising feature: the 4d index/3d partition function of a bad theory behaves as a sum of distributions rather than an ordinary function of the deformation parameters. We focus on the bad SQCD, with U(N c ) gauge group in 3d and USp(2N c ) in 4d, while in an upcoming paper we will consider linear quivers which, in the 3d case, have both unitary and special unitary bad nodes.

Keywords

• Duality in Gauge Field Theories
• Supersymmetric Gauge Theory
• Supersymmetry and Duality