Non minimal D-type conformal matter compactified on three punctured spheres

TL;DR

This paper constructs 4d Lagrangian models for compactifications of 6d conformal matter on three-punctured spheres, revealing new minimal punctures and their dualities, extending known models and providing insights into the structure of these theories.

Contribution

It introduces new 4d Lagrangian descriptions for compactified 6d conformal matter with minimal punctures, using RG flows and dualities, and generalizes known models to non-minimal cases.

Findings

Derived 4d Lagrangians for non-minimal conformal matter compactifications.

Identified new minimal punctures and confirmed their S-duality properties.

Connected the models to known minimal cases and flux tube models.

Abstract

We study compactifications of $6d$ non minimal $(D_{p+3},D_{p+3})$ type conformal matter. These can be described by $N$ M5-branes probing a $D_{p+3}$-type singularity. We derive $4d$ Lagrangians corresponding to compactifications of such $6d$ SCFTs on three punctured spheres (trinions) with two maximal punctures and one minimal puncture. The trinion models are described by simple $\mathcal{N}=1$ quivers with $SU(2N)$ gauge nodes. We derive the trinion Lagrangians using RG flows between the aforementioned $6d$ SCFTs with different values of $p$ and their relations to matching RG flows in their compactifications to $4d$. The suggested trinions are shown to reduce to known models in the minimal case of $N=1$. Additional checks are made to show the new minimal punctures uphold the expected S-duality between models in which we exchange two such punctures. We also show that closing the new minimal puncture leads to expected flux tube models.