From 6D SCFTs to Dynamic GLSMs

Abstract

Compactifications of 6D superconformal field theories (SCFTs) on four-manifolds generate a large class of novel 2d quantum field theories. We consider in detail the case of the rank one simple non-Higgsable cluster 6D SCFTs. On the tensor branch of these theories, the gauge group is simple and there are no matter fields. For compactifications on suitably chosen Kahler surfaces, we present evidence that this provides a method to realize 2d SCFTs with N = (0,2) supersymmetry. In particular, we find that reduction on the tensor branch of the 6D SCFT yields a description of the same 2d fixed point that is described in the UV by a gauged linear sigma model (GLSM) in which the parameters are promoted to dynamical fields, that is, a "dynamic GLSM" (DGLSM). Consistency of the model requires the DGLSM to be coupled to additional non-Lagrangian sectors obtained from reduction of the anti-chiral two-form of the 6D theory. These extra sectors include both chiral and anti-chiral currents, as well as spacetime filling non-critical strings of the 6D theory. For each candidate 2d SCFT, we also extract the left- and right-moving central charges in terms of data of the 6D SCFT and the compactification manifold.

v2: 72 pages, 3 figures, references and clarifications added

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• Top Down Approach to 6D SCFTs
• Universal RG Flows Across Dimensions and Holography
• Universal Features of BPS Strings in Six-dimensional SCFTs
• 6D Fractional Quantum Hall Effect
• Revisiting the classifications of 6d SCFTs and LSTs
• 4D Gauge Theories with Conformal Matter
• A slow review of the AGT correspondence
• SymTFTs and Duality Defects from 6d SCFTs on 4-manifolds
• Anomaly Inflow Methods for SCFT Constructions in Type IIB
• Algebraic Cycles and Local Anomalies in F-Theory
• Two 6d origins of 4d SCFTs: class $\mathcal{S}$ and 6d (1,0) on a torus
• Non-Simply-Connected Symmetries in 6D SCFTs
• Theories of Class F and Anomalies
• B-branes and supersymmetric quivers in 2d
• 2D CFT blocks for the 4D class ${\mathcal{S}}_k$ theories
• The Green-Schwarz Mechanism and Geometric Anomaly Relations in 2d (0,2) F-theory Vacua
• A proposal for (0,2) mirrors of toric varieties
• Geometric Approach to 3D Interfaces at Strong Coupling
• EFT of 6D SUSY RG Flows
• Elliptic Calabi-Yau fivefolds and 2d (0,2) F-theory landscape
• Geometric Approaches to Quantum Fields and Strings at Strong Couplings