Compactifications of ADE conformal matter on a torus

Abstract

In this paper we study compactifications of ADE type conformal matter, N M5 branes probing ADE singularity, on torus with flux for global symmetry. We systematically construct the four dimensional theories by first going to five dimensions and studying interfaces. We claim that certain interfaces can be associated with turning on flux in six dimensions. The interface models when compactified on a circle comprise building blocks for constructing four dimensional models associated to flux compactifications of six dimensional theories on a torus. The theories in four dimensions turn out to be quiver gauge theories and the construction implies many interesting cases of IR symmetry enhancements and dualities of such theories.

arXiv comment66 pages; 38 figures

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• Two 6d origins of 4d SCFTs: class $\mathcal{S}$ and 6d (1,0) on a torus
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• Anomaly Inflow, Accidental Symmetry, and Spontaneous Symmetry Breaking
• Infinitely many 4d N=1 SCFTs with a=c
• Elliptic Quantum Curves of Class ${\mathcal{S}}_k$
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• $\mathcal{N}=1$ Curves on Generalized Coulomb Branches
• Compactifying 5d superconformal field theories to 3d
• The Geometry of Decoupling Fields
• D-type Minimal Conformal Matter: Quantum Curves, Elliptic Garnier Systems, and the 5d Descendants
• $G_2$-Manifolds from 4d N=1 Theories, Part I: Domain Walls
• Rank $Q$ E-String on Spheres with Flux
• Aspects of 4d supersymmetric dynamics and geometry