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arXiv · 2309.05326

Probing bad theories with the dualization algorithm I

Simone Giacomelli·Chiung Hwang·Fabio Marino·Sara Pasquetti·Matteo Sacchi
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Abstract

Recently an algorithm to build $SL(2,\mathbb{Z})$ duals, including mirror duals, of 3d $\mathcal{N}=4$ quiver theories and their 4d $\mathcal{N}=1$ 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.

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Simone Giacomelli, Chiung Hwang, Fabio Marino, Sara Pasquetti, Matteo Sacchi. 2023-09-11. Probing bad theories with the dualization algorithm I. https://arxiv.org/abs/2309.05326

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