Conformal collider physics: Energy and charge correlations

TL;DR

This paper explores energy and charge correlation functions in conformal field theories, relating them to collider observables, and provides a gravity dual prescription to compute these correlations, revealing small fluctuations beyond the classical approximation.

Contribution

It introduces a method to compute energy and charge correlations in conformal theories with gravity duals, including stringy corrections and bounds on anomaly parameters.

Findings

Energy correlations are controlled by light-ray operator twists.

Charge two-point functions relate to deep inelastic scattering distributions.

Stringy corrections induce small non-Gaussian fluctuations.

Abstract

We study observables in a conformal field theory which are very closely related to the ones used to describe hadronic events at colliders. We focus on the correlation functions of the energies deposited on calorimeters placed at a large distance from the collision. We consider initial states produced by an operator insertion and we study some general properties of the energy correlation functions for conformal field theories. We argue that the small angle singularities of energy correlation functions are controlled by the twist of non-local light-ray operators with a definite spin. We relate the charge two point function to a particular moment of the parton distribution functions appearing in deep inelastic scattering. The one point energy correlation functions are characterized by a few numbers. For ${\cal N}=1$ superconformal theories the one point function for states created by the R-current or the stress tensor are determined by the two parameters $a$ and $c$ characterizing the conformal anomaly. Demanding that the measured energies are positive we get bounds on $a/c$. We also give a prescription for computing the energy and charge correlation functions in theories that have a gravity dual. The prescription amounts to probing the falling string state as it crosses the $AdS$ horizon with gravitational shock waves. In the leading, two derivative, gravity approximation the energy is uniformly distributed on the sphere at infinity, with no fluctuations. We compute the stringy corrections and we show that they lead to small, non-gaussian, fluctuations in the energy distribution. Corrections to the one point functions or antenna patterns are related to higher derivative corrections in the bulk.