Conformal Manifolds and 3d Mirrors of $(D_n,D_m)$ Theories

TL;DR

This paper explores the conformal manifolds and 3d mirror theories of a class of Argyres-Douglas theories, revealing new dualities and geometric insights through singularity analysis and gauge theory constructions.

Contribution

It provides a comprehensive analysis of conformal manifolds and constructs 3d mirror theories for all $(D_n,D_m)$ Argyres-Douglas theories, including methods to derive weakly-coupled descriptions from singularity data.

Findings

Derived 3d mirror theories for all $(D_n,D_m)$ AD theories.

Identified gauge theory descriptions involving SO and USp gaugings.

Connected crepant resolutions to symplectic gauge nodes in 3d mirrors.

Abstract

The Argyres-Douglas (AD) theories of type $(D_n,D_m)$, realized by type IIB geometrical engineering on a single hypersurface singularity, are studied. We analyze their conformal manifolds and propose the 3d mirror theories of all theories in this class upon reduction on a circle. A subclass of the AD theories in question that admits marginal couplings is found to be $\mathrm{SO}$ or $\mathrm{USp}$ gaugings of certain $D_p(\mathrm{SO}(2N))$ and $D_p(\mathrm{USp}(2N))$ theories. For such theories, we develop a method to derive this weakly-coupled description from the Newton polygon associated to the singularity. We further find that the presence of crepant resolutions of the geometry is reflected in the presence of a (non-abelian) symplectic-type gauge node in the quiver description of the 3d mirror theory. The other important results include the 3d mirrors of all $D_p(\mathrm{SO}(2N))$ theories, as well as certain properties of the $D_p(\mathrm{USp}(2N))$ theories that admit Lagrangian descriptions.