Abstract
We consider type IIB $SL(2,\mathbb{Z})$ symmetry to relate the partition functions of different 5d supersymmetric Abelian linear quiver Yang-Mills theories in the $\Omega$-background and squashed $S^5$ background. By Higgsing S-dual theories, we extract new and old 3d mirror pairs. Generically, the Higgsing procedure yields 3d defects on intersecting spaces, and we derive new hyperbolic integral identities expressing the equivalence of the squashed $S^3$ partition functions with additional degrees of freedom on the $S^1$ intersection.
Highlights
One of the most beautiful features in the family of 3d gauge theories with N 1⁄4 4 supersymmetry is the existence of mirror symmetry [1]
One of our main results is a non-Abelian version of the basic SQED/ XYZ duality. This duality has implicitly appeared in [34] as an intermediate step to test the mirror dual of ðA1; A2n−1Þ Argyres-Douglas (AD) theories reduced to 3d, which has been shown to follow from an involved cascade of sequential confinement and mirror symmetry [20,21] starting from the 3d reduction of the 4d “Lagrangian” description [35,37]
This picture provides the generalization of the non-Abelian SQCDA/XYZ duality to the more complicated geometry involving 1d degrees of freedom, and we have shown that it descends from type IIB S-duality
Summary
One of the most beautiful features in the family of 3d gauge theories with N 1⁄4 4 supersymmetry is the existence of mirror symmetry [1]. One of our main results is a non-Abelian version of the basic SQED/ XYZ duality This duality has implicitly appeared in [34] (at the level of the squashed S3 partition function) as an intermediate step to test the mirror dual of ðA1; A2n−1Þ Argyres-Douglas (AD) theories reduced to 3d, which has been shown to follow from an involved cascade of sequential confinement and mirror symmetry [20,21] starting from the 3d reduction of the 4d “Lagrangian” description [35,37]. A similar triality relation among distinct gauge theories has been recently obtained in 6d [66,67]
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
