3d $\mathcal{N}=4$ Mirror Symmetry, TQFTs, and 't Hooft Anomaly Matching

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Autori principali: Balasubramanian, Mahesh K. N., Banerjee, Anindya, Buican, Matthew, Duan, Zhihao, Ferrari, Andrea E. V., Jiang, Hongliang
Natura: Preprint
Pubblicazione: 2024
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author Balasubramanian, Mahesh K. N.
Banerjee, Anindya
Buican, Matthew
Duan, Zhihao
Ferrari, Andrea E. V.
Jiang, Hongliang
author_facet Balasubramanian, Mahesh K. N.
Banerjee, Anindya
Buican, Matthew
Duan, Zhihao
Ferrari, Andrea E. V.
Jiang, Hongliang
contents Any local unitary 3d $\mathcal{N}=4$ superconformal field theory (SCFT) has a corresponding "universal" relevant deformation that takes it to a gapped phase. This deformation preserves all continuous internal symmetries, $\mathcal{S}$, and therefore also preserves any 't Hooft anomalies supported purely in $\mathcal{S}$. We describe the resulting phase diagram in the case of SCFTs that arise as the endpoints of renormalization group flows from 3d $\mathcal{N}=4$ Abelian gauge theories with any number of $U(1)$ gauge group factors and arbitrary integer charges for the matter fields. We argue that the universal deformations take these QFTs to Abelian fractional quantum Hall states in the infrared (IR), and we explain how to match 't Hooft anomalies between the non-topological ultraviolet theories and the IR topological quantum field theories (TQFTs). Along the way, we give a proof that 3d $\mathcal{N}=4$ mirror symmetry of our Abelian gauge theories descends to a duality of these TQFTs. Finally, using our anomaly matching discussion, we describe how to connect, via the renormalization group, abstract local unitary 3d $\mathcal{N}=4$ SCFTs with certain 't Hooft anomalies for their internal symmetries to IR phases (partially) described by Abelian spin Chern-Simons theories.
format Preprint
id arxiv_https___arxiv_org_abs_2412_21066
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle 3d $\mathcal{N}=4$ Mirror Symmetry, TQFTs, and 't Hooft Anomaly Matching
Balasubramanian, Mahesh K. N.
Banerjee, Anindya
Buican, Matthew
Duan, Zhihao
Ferrari, Andrea E. V.
Jiang, Hongliang
High Energy Physics - Theory
Strongly Correlated Electrons
Quantum Physics
Any local unitary 3d $\mathcal{N}=4$ superconformal field theory (SCFT) has a corresponding "universal" relevant deformation that takes it to a gapped phase. This deformation preserves all continuous internal symmetries, $\mathcal{S}$, and therefore also preserves any 't Hooft anomalies supported purely in $\mathcal{S}$. We describe the resulting phase diagram in the case of SCFTs that arise as the endpoints of renormalization group flows from 3d $\mathcal{N}=4$ Abelian gauge theories with any number of $U(1)$ gauge group factors and arbitrary integer charges for the matter fields. We argue that the universal deformations take these QFTs to Abelian fractional quantum Hall states in the infrared (IR), and we explain how to match 't Hooft anomalies between the non-topological ultraviolet theories and the IR topological quantum field theories (TQFTs). Along the way, we give a proof that 3d $\mathcal{N}=4$ mirror symmetry of our Abelian gauge theories descends to a duality of these TQFTs. Finally, using our anomaly matching discussion, we describe how to connect, via the renormalization group, abstract local unitary 3d $\mathcal{N}=4$ SCFTs with certain 't Hooft anomalies for their internal symmetries to IR phases (partially) described by Abelian spin Chern-Simons theories.
title 3d $\mathcal{N}=4$ Mirror Symmetry, TQFTs, and 't Hooft Anomaly Matching
topic High Energy Physics - Theory
Strongly Correlated Electrons
Quantum Physics
url https://arxiv.org/abs/2412.21066