More on the Matter of 6D SCFTs

TL;DR

This paper examines the scaling dimensions of the brane recombination operator in $6D$ SCFTs engineered by M5-branes probing ADE singularities. Using F-theory geometry, the holomorphic three-form $\\Omega$ scaling, and the relation $\\Delta_{6D}=\\frac{4}{3}\\Delta_{5D,KK}$, it analyzes collisions of ADE singularities and brane recombination as operator vevs. For generalized quivers $\\mathcal{T}(G,N)$, it resolves the $C^2/\\mathbb{Z}_N$ singularity and shows $\\dim r_{(N)}=\\{24N,16N,12N,8N,4N\\}$ for $(E_8,E_8),(E_7,E_7),(E_6,E_6),(D_p,D_p),(A_k,A_k)$ (with $N\ge2$ for A-type). In all applicable cases the brane-recombination operator has scaling dimension at least six, implying a marginally irrelevant deformation at the interacting fixed points, and the results illuminate the role of conformal matter in generalized quivers.

Abstract

M5-branes probing an ADE singularity lead to 6D SCFTs with (1,0) supersymmetry. On the tensor branch, the M5-branes specify domain walls of a 7D Super Yang-Mills theory with gauge group G of ADE-type, thus providing conformal matter for a broad class of generalized quiver theories. Additionally, these theories have G x G flavor symmetry, and a corresponding Higgs branch. In this note we use the F-theory realization of these theories to calculate the scaling dimension of the operator parameterizing seven-brane recombination, i.e. motion of the stack of M5-branes off of the orbifold singularity. In all cases with an interacting fixed point, we find that this operator has scaling dimension at least six, and defines a marginal irrelevant deformation.