Energy Correlator Conformal Blocks and Positivity

TL;DR

This paper advances the understanding of energy-energy correlators in conformal field theories by developing conformal blocks for arbitrary spin operators, analyzing OPE convergence, and deriving new bounds on OPE coefficients using positivity constraints.

Contribution

It provides explicit conformal blocks for energy correlators with arbitrary spin, studies OPE convergence, and establishes new bounds on OPE coefficients in CFTs, including the 3d Ising model.

Findings

Derived general conformal blocks for traceless symmetric operators of arbitrary spin.

Analyzed the convergence of the source-detector OPE in tensor product CFTs.

Obtained new bounds on OPE coefficients involving the stress-energy tensor, applied to the 3d Ising CFT.

Abstract

Correlation functions of energy flow operators (energy-energy correlators) are one of the simplest observables in quantum field theory and gravity, with diverse applications ranging from real world collider physics to constraining the space of consistent theories. In this paper we further develop the conformal block decomposition of energy-energy correlators in conformal field theories (CFTs), focusing on the source-detector operator product expansion (OPE). We compute the general conformal blocks in this channel for traceless symmetric operators of arbitrary spin in the background of a scalar source, considering both parity-even and parity-odd contributions. Motivated by the availability of data from the conformal bootstrap, we analyze the convergence of this source-detector OPE, taking a tensor product of two decoupled CFTs as an elementary example. Finally, we use positivity of energy correlators to derive novel bounds on OPE coefficients involving the stress-energy tensor in generic CFTs, and demonstrate the application of these bounds in the specific example of the 3d Ising CFT, obtaining new constraints for both parity-even and parity-odd operators.