Multi-stress tensors and next-to-leading singularities in the Regge limit

TL;DR

This paper analyzes multi-stress tensor contributions to scalar correlators in large central charge CFTs, revealing their role in Regge limit singularities and confirming results with shockwave and bootstrap methods.

Contribution

It provides a comprehensive all-orders analysis of multi-stress tensor effects on Regge singularities in four-dimensional CFTs, connecting bulk phase shifts with boundary correlator singularities.

Findings

Leading singularities match shockwave background results.

Next-to-leading singularities align with lightcone bootstrap predictions.

Multi-stress tensor contributions are characterized to all orders in 4D.

Abstract

The stress tensor sector of a heavy-heavy-light-light scalar correlator in CFTs with a large central charge and a large gap is defined by the exchange of multi-stress tensor operators. The Regge limit of this correlator is determined by the phase shift of a highly energetic particle propagating in a dual black hole background. Assuming Einstein gravity in the bulk, the phase shift is known perturbatively to all orders in the ratio of the heavy scaling dimension over the central charge. In the CFT, the order counts the number of stress tensors in the multi-stress tensor operator. By Fourier transforming the correlator to position space, the multi-stress tensor contributions to the leading and next-to-leading singularities in the Regge limit are found to all orders in four dimensions. The leading singularity at each order agrees with known results obtained by considering a particle in a dual shockwave background. Moreover, the leading and next-to-leading singularities due to double- and triple-stress tensors with minimal twist are known from lightcone bootstrap and agree with the results derived from the phase shift.