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

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.

arXiv comment28 pages, 12 figures. Minor text revisions

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• Trinions for the $3d$ compactification of the $5d$ rank 1 $E_{N_f+1}$ SCFTs
• Compactifying 5d superconformal field theories to 3d
• $G_2$-Manifolds from 4d N=1 Theories, Part I: Domain Walls
• Aspects of 4d supersymmetric dynamics and geometry