Four-Dimensional SCFTs from M5-Branes

TL;DR

The authors construct a large class of four-dimensional $\,\mathcal{N}=1\,$ SCFTs by wrapping M5-branes on complex curves and analyze them via three complementary viewpoints: a geometric twist in six dimensions, holographic AdS$_5$ backgrounds, and four-dimensional generalized quivers built from $T_N$ blocks. They derive central charges from the M5 anomaly polynomial, perform $a$-maximization to fix the superconformal R-symmetry, and reproduce the gravity results in the large-$N$ limit, including a continuous family of fixed points labeled by a twist parameter $z$. The holographic duals in eleven dimensions reveal AdS$_5$ vacua and RG flows from AdS$_7$-like UV regions, with marginal deformations counted both from complex structure moduli of $\mathcal{C}_g$ and flat connections on the curve. The generalized-quiver construction confirms the field theory content of these fixed points, yields exact central charges matching the gravity and anomaly computations, and exposes a rich conformal-manifold structure governed by $4g-3$ marginal directions, while genus-three examples highlight intriguing UV ambiguities that point to nontrivial chiral-ring relations in $T_N$ theories. Overall, the work substantially expands the landscape of known non-Lagrangian $\mathcal{N}=1$ SCFTs and links geometric, holographic, and field-theoretic descriptions in a coherent framework.

Abstract

We engineer a large new set of four-dimensional N=1 superconformal field theories by wrapping M5-branes on complex curves. We present new supersymmetric AdS_5 M-theory backgrounds which describe these fixed points at large N, and then directly construct the dual four-dimensional CFTs for a certain subset of these solutions. Additionally, we provide a direct check of the central charges of these theories by using the M5-brane anomaly polynomial. This is a companion paper which elaborates upon results reported in arXiv:1112:5487.

Figures (7)

• Figure 1: The central charge a as a function of the twist parameter $z$ for genus $g=7$, $G=A_{N-1}$, and $N=4,5,6$ (bottom to top). The MN theories are marked with large points at $z=0$ and $|z|=1$.
• Figure 2: Numerical solutions for $g(\rho)$, $\lambda_1(\rho)$ and $\lambda_2(\rho)$ (from left to right). We have fixed $\kappa=-1$ and have chosen four representative solutions for $g=7$ and $z=\{\tfrac{1}{6},\tfrac{2}{3},\tfrac{4}{3},\tfrac{10}{3}\}$.
• Figure 3: The central charge $\tilde{c}$ as a function of $z$ for $\kappa=-1$ and $g=7$.
• Figure 4: The simplest generalized quiver diagram, showing two $T_N$ theories (represented by triangles, i.e., trinions) connected by a vector multiplet (represented by a circle).
• Figure 5: $T_N$'s connected by vector multiplets.