6D SCFTs, 4D SCFTs, Conformal Matter, and Spin Chains

Abstract

Recent work has established a uniform characterization of most 6D SCFTs in terms of generalized quivers with conformal matter. Compactification of the partial tensor branch deformation of these theories on a $T^2$ leads to 4D $\mathcal{N}=2$ SCFTs which are also generalized quivers. Taking products of bifundamental conformal matter operators, we present evidence that there are large R-charge sectors of the theory in which operator mixing is captured by a 1D spin chain Hamiltonian with operator scaling dimensions controlled by a perturbation series in inverse powers of the R-charge. We regulate the inherent divergences present in the 6D computations with the associated 5D Kaluza--Klein theory. In the case of 6D SCFTs obtained from M5-branes probing a ${\mathbb{C}}^2/{\mathbb{Z}}_K$ singularity, we show that there is a class of operators where the leading order mixing effects are captured by the integrable Heisenberg $XX{X}_{s=1/2}$ spin chain with open boundary conditions, and similar considerations hold for its $T^2$ reduction to a 4D $\mathcal{N}=2$ SCFT. In the case of M5-branes probing more general D- and E-type singularities where generalized quivers have conformal matter, we argue that similar mixing effects are captured by an integrable $XX{X}_s$ spin chain with $s>1/2$. We also briefly discuss some generalizations to other operator sectors as well as little string theories.

v4: 52 pages, 5 figures, typos corrected

References in corpus (5)

• Anomaly polynomial of general 6d SCFTs
• Supersymmetric gauge theory and the Yangian
• All Tree-Level Correlators for M-theory on $Ad{S}_7\times S^4$
• Integrability and Holographic Aspects of Six-Dimensional $\mathcal{N}=(1,0)$ Superconformal Field Theories
• 6d $\mathcal{N}=(1,0)$ theories on $T^2$ and class S theories: part I

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