Lessons from crossing symmetry at large N

2014/10/17 by Luis F. Alday, Alday, Luis F., Agnese Bissi +3 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions

paper · doi:10.48550/arxiv.1410.4717

openalex publication_date 2014/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the four-point correlator of the stress tensor multiplet in N=4 SYM. We construct all solutions consistent with crossing symmetry in the limit of large central charge c ~ N² and large g² N. While we find an infinite tower of solutions, we argue most of them are suppressed by an extra scale Δ_gap and are consistent with the upper bounds for the scaling dimension of unprotected operators observed in the numerical superconformal bootstrap at large central charge. These solutions organize as a double expansion in 1/c and 1/Δ_gap. Our solutions are valid to leading order in 1/c and to all orders in 1/Δ_gap and reproduce, in particular, instanton corrections previously found. Furthermore, we find a connection between such upper bounds and positivity constraints arising from causality in flat space. Finally, we show that certain relations derived from causality constraints for scattering in AdS follow from crossing symmetry.

Citations

• D-independent representation of Conformal Field Theories in D dimensions via transformation to auxiliary Dual Resonance Models. Scalar amplitudes
• Causality, Analyticity and an IR Obstruction to UV Completion

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• ε-Expansions Near Three Dimensions from Conformal Field Theory

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