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Lessons from crossing symmetry at large N
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Lessons from crossing symmetry at large N
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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 ~ N^2 and large g^2 N. While we find an infinite tower of solutions, we argue most of them are suppressed by an extra scale \Delta_{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/\Delta_{gap}. Our solutions are valid to leading order in 1/c and to all orders in 1/\Delta_{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.
Forward citations
Cited by 2 Pith papers
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Neural Spectral Bias and Conformal Correlators I: Introduction and Applications
Neural networks optimized solely on crossing symmetry reconstruct CFT correlators from minimal input data to few-percent accuracy across generalized free fields, minimal models, Ising, N=4 SYM, and AdS diagrams.
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Higher-Trace Operators and Cut Diagrammatics in the Conformal Block Expansion
Introduces a cut-diagrammatic framework to apply crossing symmetry to individual topologies in large-N CFT correlators and computes associated OPE data for higher-trace operators.
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