Non-Abelian Binding Energies from the Lightcone Bootstrap

TL;DR

This paper analytically explores the lightcone bootstrap for 4-point scalar functions with global symmetries, revealing universal binding energies and the necessity of higher spin currents in certain large symmetry limit conformal field theories.

Contribution

It provides new analytical results on anomalous dimensions of double-twist operators and their interpretation as binding energies in AdS, highlighting universality and symmetry-dependent features.

Findings

Gravity induces universal attractive binding energies.

Gauge interactions can be attractive or repulsive depending on representation.

Infinite higher spin currents are required in certain large symmetry limits.

Abstract

We analytically study the lightcone limit of the conformal bootstrap for 4-point functions containing scalars charged under global symmetries. We show the existence of large spin double-twist operators in various representations of the global symmetry group. We then compute their anomalous dimensions in terms of the central charge $C_T$, current central charge $C_J$, and the OPE coefficients of low dimension scalars. In AdS, these results correspond to the binding energy of two-particle states arising from the exchange of gravitons, gauge bosons, and light scalar fields. Using unitarity and crossing symmetry, we show that gravity is universal and attractive among different types of two-particle states, while the gauge binding energy can have either sign as determined by the representation of the two-particle state, with universal ratios fixed by the symmetry group. We apply our results to 4D $\mathcal{N}=1$ SQCD and the 3D O(N) vector models. We also show that in a unitary CFT, if the current central charge $C_J$ stays finite when the global symmetry group becomes infinitely large, such as the $N\rightarrow\infty$ limit of the O(N) vector model, then the theory must contain an infinite number of higher spin currents.