Non-Abelian Binding Energies from the Lightcone Bootstrap

TL;DR

This work extends the analytic lightcone bootstrap to CFTs with non-Abelian global symmetries, deriving universal and representation-dependent binding-energy corrections for large-spin double-twist operators in terms of $C_T$, $C_J$, and low-dimension OPE data. It reveals gravity-like universal negative binding energies across representations and gauge-binding energies whose sign and magnitude are fixed by group structure, with charged-scalar exchanges introducing spin-dependent sign patterns. The results are applied to 4D $ ext{N}=1$ SQCD and 3D $O(N)$ vector models, including Veneziano-limit behavior and large-$N$ implications for higher-spin currents. The analysis also motivates a sharp condition: if $C_J$ remains finite at large $N$, the CFT must possess an infinite tower of higher-spin conserved currents, linking bootstrap consistency to the emergence of higher-spin symmetries in the dual AdS description.

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.