Aspects of superconformal field theories in six dimensions

Abstract

We introduce the analytic superspace formalism for six-dimensional $(N,0)$ superconformal field theories. Concentrating on the $(2,0)$ theory we write down the Ward identities for correlation functions in the theory and show how to solve them. We then consider the four-point function of four energy momentum multiplets in detail, explicitly solving the Ward identities in this case. We expand the four-point function using both Schur polynomials, which lead to a simple formula in terms of a single function of two variables, and (a supersymmetric generalisation of) Jack polynomials, which allow a conformal partial wave expansion. We then perform a complete conformal partial wave analysis of both the free theory four-point function and the AdS dual four-point function. We also discuss certain operators at the threshold of the series a) unitary bound, and prove that some such operators may not develop anomalous dimensions, by finding selection rules for certain three-point functions. For those operators which are not protected, we find representations with which they may combine to become long.

37 pages. References added

References in corpus (7)

• Conformal Partial Waves and the Operator Product Expansion
• On Short and Semi-Short Representations for Four Dimensional Superconformal Symmetry
• Correlation Functions and Massive Kaluza-Klein Modes in the AdS/CFT Correspondence
• Four-point functions in N=4 SYM
• Systematics of Quarter BPS operators in N=4 SYM
• Aspects of N=4 SYM
• Four-point correlators of BPS operators in N=4 SYM at order g^4

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• Bootstrapping Mixed Correlators in the 3D Ising Model
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• On Four-Point Functions of Half-BPS Operators in General Dimensions
• Holographic Reconstruction of AdS Exchanges from Crossing Symmetry
• M-Theory Reconstruction from (2,0) CFT and the Chiral Algebra Conjecture
• 6d (2,0) and M-theory at 1-loop
• The SAGEX Review on Scattering Amplitudes, Chapter 8: Half BPS correlators
• Superconformal partial waves in Grassmannian field theories
• M-theory Beyond The Supergravity Approximation
• 6D (2,0) Bootstrap with soft-Actor-Critic
• Notes on Super Killing Tensors
• Five-Dimensional Non-Lorentzian Conformal Field Theories and their Relation to Six-Dimensions
• Bootstrapping string dynamics in the 6d $\mathcal{N}=(2,0)$ theories
• Regge trajectories for the (2,0) theories
• Recursion Relations for Anomalous Dimensions in the 6d $(2,0)$ Theory
• Pure anti-de Sitter supergravity and the conformal bootstrap
• Five-Dimensional Path Integrals for Six-Dimensional Conformal Field Theories
• Superconformal blocks in diverse dimensions and $BC$ symmetric functions
• Instanton Worldlines in Five-Dimensional $\Omega$-Deformed Gauge Theory
• Superconformal Block from Holographic Geometry
• The $\mathcal{W}$-algebra bootstrap of 6d $\mathcal{N}=(2,0)$ theories