Probing bad theories with the dualization algorithm. Part I
Simone Giacomelli, Chiung Hwang, Fabio Marino, Sara Pasquetti, Matteo Sacchi
Abstract
A bstract Recently an algorithm to build SL(2, ℤ) duals, including mirror duals, of 3d $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 4 quiver theories and their 4d $$ \mathcal{N} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>N</mml:mi> </mml:math> = 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(2 N 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.