6d Conformal Matter

TL;DR

We address the construction of 6d $(1,0)$ SCFTs from M5-branes probing ADE singularities, introducing conformal-matter sectors with $G\times G$ symmetry and their realization on domain walls in 7d SYM. The work develops F-theory descriptions of the tensor/Coulomb branches, identifies fractional M5-brane phenomena, and analyzes partial Higgs branches via T-brane boundary data, extended to E8 walls and heterotic duals. It further derives 5d dual descriptions from circle reductions, proposes 6d dualities inferred from 5d correspondences, and constructs holographic duals in M-theory/IIA with scaling limits, including orientifolds. Overall, the paper provides a unified geometric and brane-based framework for non-Lagrangian 6d fixed points, their lower-dimensional reductions, and their gravity duals, with broad implications for generalized quiver theories and conformal matter.

Abstract

A single M5-brane probing G, an ADE-type singularity, leads to a system which has G x G global symmetry and can be viewed as "bifundamental" (G,G) matter. For the A_N series, this leads to the usual notion of bifundamental matter. For the other cases it corresponds to a strongly interacting (1,0) superconformal system in six dimensions. Similarly, an ADE singularity intersecting the Horava-Witten wall leads to a superconformal matter system with E_8 x G global symmetry. Using the F-theory realization of these theories, we elucidate the Coulomb/tensor branch of (G,G') conformal matter. This leads to the notion of fractionalization of an M5-brane on an ADE singularity as well as fractionalization of the intersection point of the ADE singularity with the Horava-Witten wall. Partial Higgsing of these theories leads to new 6d SCFTs in the infrared, which we also characterize. This generalizes the class of (1,0) theories which can be perturbatively realized by suspended branes in IIA string theory. By reducing on a circle, we arrive at novel duals for 5d affine quiver theories. Introducing many M5-branes leads to large N gravity duals.

Figures (10)

• Figure 1: up: $N$ M5-branes at an orbifold singularity (SCFT point). down: The Coulomb/tensor branch deformation where the $N$ M5-branes are separated along the singularity locus and associated conformal matter which are symbolically represented by wavy lines between adjacent gauge factors.
• Figure 2: Example of two M5-branes probing an $E_8$ singularity. Moving onto the tensor branch gives rise to $(E_8,E_8)$ conformal matter that are SCFTs themselves with their own tensor branches, as described by the generalized quiver of line \ref{['GQE8E8']}. This suggests that each M5-brane on $E_8$ has fractionated to 12 pieces.
• Figure 3: Type IIA description of the system of $N$ M5-branes probing the $\mathbb{C}^{2}/\mathbb{Z}_{k}$ singularity: here we are drawing schematically the $X^{6}$ direction for the tensor branch. One obtains $N$ NS5-branes sitting on top of $k$ infinite D6 branes.
• Figure 4: An instance of a novel 5d duality. The 6d theory of two M5-branes probing an $E_8$ singularity (top) compactified on $S^1$ is dual to the affine $\widehat{E}_8(2)$ 5d quiver system (bottom).
• Figure 5: A brane configuration similar to figure \ref{['noD8HZ']}, where now the D6s end on D8s in two different ways on the two sides, corresponding to two different Young diagrams. This configuration is T-dual to the one in figure \ref{['fig:D7Hpoles']}.