Dualities and loops on squashed $S^3$

Abstract

We consider $\mathcal{N}=4$ supersymmetric gauge theories on the squashed three-sphere with six preserved supercharges. We first discuss how Wilson and vortex loops preserve up to four of the supercharges and we find squashing independence for the expectation values of these $\frac{2}{3}$-BPS loops. We then show how the additional supersymmetries facilitate the analytic matching of partition functions and loop operator expectation values to those in the mirror dual theory, allowing one to lift all the results that were previously established on the round sphere to the squashed sphere. Additionally, on the squashed sphere with four preserved supercharges, we numerically evaluate the partition functions of ABJM and its dual super-Yang-Mills at low ranks of the gauge group. We find matching values of their partition functions, prompting us to conjecture the general equality on the squashed sphere. From the numerics we also observe the squashing dependence of the Lee-Yang zeros and of the non-perturbative corrections to the all order large $N$ expression for the ABJM partition function.

v3: corrected typos, clarified language, added 2 figures, v2: added references and corrected typos, v1: 17 pages, 3 appendices, 18 figures, 3 videos availabe at https://youtube.com/playlist?list=PL2-qyK_VoDsL0T98yxySNCW-QFVaNNNoN

References in corpus (15)

• Notes on SUSY Gauge Theories on Three-Sphere
• Seiberg Duality in Chern-Simons Theory
• Summing Up All Genus Free Energy of ABJM Matrix Model
• Large $N$ Partition Functions of the ABJM Theory
• Hanany-Witten effect and SL(2,Z) dualities in matrix models
• 4d $S$-duality wall and $SL(2,\mathbb{Z})$ relations
• Rethinking mirror symmetry as a local duality on fields
• The $SL(2,\mathbb{Z})$ dualization algorithm at work
• Squashing and supersymmetry enhancement in three dimensions
• ABJ Wilson loops and Seiberg Duality
• One-Dimensional Sectors From the Squashed Three-Sphere
• Classifying BPS bosonic Wilson loops in 3d $\mathcal{N}=4$ Chern-Simons-matter theories
• Exploring Seiberg-like Dualities with Eight Supercharges
• $S^1$ Reduction of 4D $\mathcal{N}=3$ SCFTs and Squashing Independence of ABJM Theories
• Exploring Seiberg-like N-alities with Eight Supercharges