The $SL(2,\mathbb{Z})$ dualization algorithm at work

Riccardo Comi; Chiung Hwang; Fabio Marino; Sara Pasquetti; Matteo Sacchi

doi:10.1007/JHEP06(2023)119

paper

The $S L (2, Z)$ dualization algorithm at work

arXiv:2212.10571 · doi:10.1007/JHEP06(2023)119

Abstract

Recently an algorithm to dualize a theory into its mirror dual has been proposed, both for $3 d$ $N = 4$ linear quivers and for their $4 d$ $N = 1$ uplift. This mimics the manipulations done at the level of the Type IIB brane setup that engineers the $3 d$ theories, where mirror symmetry is realized as $S$ -duality, but it is enirely field-theoretic and based on the application of genuine infra-red dualities that implement the local action of $S$ -duality on the quiver. In this paper, we generalize the algorithm to the full duality group, which is $S L (2, Z)$ in $3 d$ and $P S L (2, Z)$ in $4 d$ . This also produces dualities for $3 d$ $N = 3$ theories with Chern--Simons couplings, some of which have enhanced $N = 4$ supersymmetry, and their new $4 d$ $N = 1$ counterpart. In addition, we propose three ways to study the RG flows triggered by possible VEVs appearing at the last step of the algorithm, one of which uses a new duality that implements the Hanany--Witten move in field theory.

arXiv comment79 plus 27 pages, 95 figures; v2: paragraph added to the introduction, a few figures modified, figure with an example of application of the algorithm in 3d added, references added

The $S L (2, Z)$ dualization algorithm at work

Abstract

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The SL(2,Z) dualization algorithm at work

Abstract

References in corpus (89)

Cited by in corpus (3)

The $S L (2, Z)$ dualization algorithm at work