MSW-type compactifications of 6d $(1,0)$ SCFTs on 4-manifolds

TL;DR

This paper explores the compactification of 6d (1,0) SCFTs on Kähler 4-manifolds, deriving 2d SCFTs and their central charges using anomaly polynomials and topological twists, with applications to domain walls and coupled systems.

Contribution

It introduces a novel framework for compactifying 6d SCFTs on 4-manifolds, connecting M5 brane configurations to 2d SCFTs and analyzing their anomalies and central charges.

Findings

Derived central charges of 2d SCFTs from 6d anomaly polynomials.

Established a method to glue non-compact 4-manifold compactifications to reproduce anomalies.

Proposed concrete 2d CFT models for specific compactification cases.

Abstract

In this work, we study compactifications of 6d $(1,0)$ SCFTs, in particular those of conformal matter type, on K\"ahler 4-manifolds. We show how this can be realized via wrapping M5 branes on 4-cycles of non-compact Calabi-Yau fourfolds with ADE singularity in the fiber. Such compactifications lead to domain walls in 3d $\mathcal{N}=2$ theories which flow to 2d $\mathcal{N}=(0,2)$ SCFTs. We compute the central charges of such 2d CFTs via 6d anomaly polynomials by employing a particular topological twist along the 4-manifold. Moreover, we study compactifications on non-compact 4-manifolds leading to coupled 3d-2d systems. We show how these can be glued together consistently to reproduce the central charge and anomaly polynomial obtained in the compact case. Lastly, we study concrete CFT proposals for some special cases.