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

Federico Carta, Simone Giacomelli, Noppadol Mekareeya, Alessandro Mininno

TL;DR

The authors systematically analyze the conformal manifolds of (D_n,D_m) Argyres-Douglas theories engineered by a single hypersurface singularity and derive their 3d mirrors upon circle reduction. They identify weakly coupled cusps via a Newton-polygon approach and link crepant resolutions to a symplectic-type USp gauge node in the 3d quiver, providing a unified picture for how Higgs- and Coulomb-branch data match across dimensions. The work delivers explicit 3d mirrors for D_p(SO(2N)) and D_p(USp(2N)) theories, and builds a comprehensive framework to construct 3d mirrors of all (D_n,D_m) theories, organized by the number of mass parameters, including detailed examples and non-Higgsable SCFT identifications. This yields new dual descriptions and strengthens the connection between IIB geometry, moduli spaces of SCFTs, and 3d $ ixmathcal N=4$ gauge dynamics, with potential implications for class S constructions and Higgs-branch geometry. Overall, it advances a geometric-programmatic method to extract Lagrangian and quiver-mirror data from higher-dimensional non-Lagrangian theories.

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.

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

TL;DR

The authors systematically analyze the conformal manifolds of (D_n,D_m) Argyres-Douglas theories engineered by a single hypersurface singularity and derive their 3d mirrors upon circle reduction. They identify weakly coupled cusps via a Newton-polygon approach and link crepant resolutions to a symplectic-type USp gauge node in the 3d quiver, providing a unified picture for how Higgs- and Coulomb-branch data match across dimensions. The work delivers explicit 3d mirrors for D_p(SO(2N)) and D_p(USp(2N)) theories, and builds a comprehensive framework to construct 3d mirrors of all (D_n,D_m) theories, organized by the number of mass parameters, including detailed examples and non-Higgsable SCFT identifications. This yields new dual descriptions and strengthens the connection between IIB geometry, moduli spaces of SCFTs, and 3d gauge dynamics, with potential implications for class S constructions and Higgs-branch geometry. Overall, it advances a geometric-programmatic method to extract Lagrangian and quiver-mirror data from higher-dimensional non-Lagrangian theories.

Abstract

The Argyres-Douglas (AD) theories of type , 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 or gaugings of certain and 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 theories, as well as certain properties of the theories that admit Lagrangian descriptions.

Paper Structure

This paper contains 30 sections, 128 equations.

Table of Contents

  1. Introduction
  2. Notation and convention
  3. The conformal manifold for $(D,D)$ Argyres-Douglas theories
  4. Counting mass deformations
  5. Counting crepant divisors
  6. The 3d mirror of $D_p(\mathrm{SO}(2N))$ theories with $p<2N-2$
  7. $D_p(\mathrm{SO}(2N))$ theories with $p$ odd
  8. $D_p(\mathrm{SO}(2N))$ theories with $p$ even
  9. The case $\frac{2N-2}{\mathrm{GCD}(2N-2,p)}$ even
  10. The case $\frac{2N-2}{\mathrm{GCD}(2N-2,p)}$ odd
  11. The 3d mirror of $(D_n,D_m)$ theories
  12. Theories with $1$ mass parameter
  13. Derivation of the 3d mirror for $\left(D_{4\mathfrak{n}-1},D_{4\mathfrak{m}+4\mathfrak{n}-3}\right)$
  14. Theories with $2$ mass parameters
  15. The special case of $(D_3, D_{2\mathfrak{n}+2})\cong (A_3, D_{2\mathfrak{n}+2})$ theories
  16. ...and 15 more sections