Convexity and Liberation at Large Spin

Abstract

We consider several aspects of unitary higher-dimensional conformal field theories (CFTs). We first study massive deformations that trigger a flow to a gapped phase. Deep inelastic scattering in the gapped phase leads to a convexity property of dimensions of spinning operators of the original CFT. We further investigate the dimensions of spinning operators via the crossing equations in the light-cone limit. We find that, in a sense, CFTs become free at large spin and 1/s is a weak coupling parameter. The spectrum of CFTs enjoys additivity: if two twists tau_1, tau_2 appear in the spectrum, there are operators whose twists are arbitrarily close to tau_1+tau_2. We characterize how tau_1+tau_2 is approached at large spin by solving the crossing equations analytically. We find the precise form of the leading correction, including the prefactor. We compare with examples where these observables were computed in perturbation theory, or via gauge-gravity duality, and find complete agreement. The crossing equations show that certain operators have a convex spectrum in twist space. We also observe a connection between convexity and the ratio of dimension to charge. Applications include the 3d Ising model, theories with a gravity dual, SCFTs, and patterns of higher spin symmetry breaking.

61 pages, 13 figures. v2: added reference and minor correction

References in corpus (14)

• Causality, Analyticity and an IR Obstruction to UV Completion
• Holography from Conformal Field Theory
• Conformal collider physics: Energy and charge correlations
• The Bootstrap Program for Boundary CFT_d
• Bounds on 4D Conformal and Superconformal Field Theories
• Comments on operators with large spin
• Comments on Unparticles
• Eikonal Approximation in AdS/CFT: Resumming the Gravitational Loop Expansion
• Eikonal Approximation in AdS/CFT: Conformal Partial Waves and Finite N Four-Point Functions
• Limit Cycles and Conformal Invariance
• Conformal Blocks for Arbitrary Spins in Two Dimensions
• Black holes and universality classes of critical points
• Limit Cycles in Four Dimensions
• On Limit Cycles in Supersymmetric Theories

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