From 6D SCFTs to Dynamic GLSMs

TL;DR

This paper explores how compactifying certain 6D superconformal field theories on four-manifolds leads to novel 2D quantum field theories with (0,2) supersymmetry, introducing the concept of dynamic GLSMs coupled to non-Lagrangian sectors.

Contribution

It introduces the idea of dynamic GLSMs arising from 6D SCFT compactifications and details their coupling to non-Lagrangian sectors from the 6D anti-chiral two-form reduction.

Findings

Reduction yields 2D SCFTs with calculable central charges.

Dynamic GLSMs encode the same fixed points as UV descriptions.

Coupling to non-Lagrangian sectors is essential for consistency.

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.