Aspects of 3d N=2 Chern-Simons-Matter Theories

TL;DR

This paper explores the dynamics, phases, and dualities of 3d N=2 Chern-Simons-matter theories, analyzing their vacua, monopole operators, and solitons, and establishing connections between different dualities.

Contribution

It provides a detailed analysis of the phases, monopole operators, and dualities in 3d N=2 Chern-Simons-matter theories, including derivations of Aharony duality from Giveon-Kutasov duality.

Findings

Witten index remains invariant across phase transitions.

Solitons are compatible with mirror symmetry exchanging Higgs and Coulomb branches.

Aharony duality can be derived from Giveon-Kutasov duality.

Abstract

We comment on various aspects of the the dynamics of 3d N=2 Chern-Simons gauge theories and their possible phases. Depending on the matter content, real masses and FI parameters, there can be non-compact Higgs or Coulomb branches, compact Higgs or Coulomb branches, and isolated vacua. We compute the Witten index of the theories, and show that it does not change when the system undergoes a phase transition. We study aspects of monopole operators and solitons in these theories, and clarify subtleties in the soliton collective coordinate quantization. We show that solitons are compatible with a mirror symmetry exchange of Higgs and Coulomb branches, with BPS solitons on one branch related to the modulus of the other. Among other results, we show how to derive Aharony duality from Giveon-Kutasov duality.