A New Spin on Causality Constraints

TL;DR

This paper explores how causality constraints in conformal field theories relate to the analytic properties of correlation functions, extending known energy conditions to non-holographic theories and involving light spinning operators.

Contribution

It extends causality constraints to light spinning operators in CFTs and links these to energy interactions, broadening the scope beyond scalar probes and holographic theories.

Findings

Constraints on stress tensor couplings to light spinning operators.

Subset of Hofman-Maldacena conditions for positive energy.

Extension of causality-energy relation to non-holographic theories.

Abstract

Causality in a shockwave state is related to the analytic properties of a four-point correlation function. Extending recent results for scalar probes, we show that this constrains the couplings of the stress tensor to light spinning operators in conformal field theory, and interpret these constraints in terms of the interaction with null energy. For spin-1 and spin-2 conserved currents in four dimensions, the resulting inequalities are a subset of the Hofman-Maldacena conditions for positive energy deposition. It is well known that energy conditions in holographic theories are related to causality on the gravity side; our results make a connection on the CFT side, and extend it to non-holographic theories.