# Probing Universalities in d>2 CFTs: from Black Holes to Shockwaves

## TL;DR

This paper demonstrates a universal structure in higher-dimensional conformal field theories by showing the insensitivity of certain OPE coefficients and correlators to higher-curvature corrections, linking black hole and shockwave limits.

## Contribution

It provides explicit calculations and recursion relations for stress-tensor OPE coefficients, revealing their universality and connection between black hole and shockwave regimes in holographic CFTs.

## Key findings

- OPE coefficients are insensitive to higher-curvature corrections.
- Shockwave and black hole correlator limits agree after resummation.
- ANEC exponentiation occurs in the multi-stress-tensor sector.

## Abstract

Gravitational shockwaves are insensitive to higher-curvature corrections in the action. Recent work found that the OPE coefficients of lowest-twist multi-stress-tensor operators, computed holographically in a planar black hole background, are insensitive as well. In this paper, we analyze the relation between these two limits. We explicitly evaluate the two-point function on a shockwave background to all orders in a large central charge expansion. In the geodesic limit, we find that the ANEC exponentiates in the multi-stress-tensor sector. To compare with the black hole limit, we obtain a recursion relation for the lowest-twist products of two stress tensors in a spherical black hole background, letting us efficiently compute their OPE coefficients and prove their insensitivity to higher curvature terms. After resumming the lowest-twist stress-tensors and analytically continuing their contributions to the Regge limit, we find a perfect agreement with the shockwave computation. We also discuss the role of double-trace operators, global degenerate states, and multi-stress-tensor conformal blocks. These holographic results suggest the existence of a larger universal structure in higher-dimensional CFTs.