Comb channel lightcone bootstrap: triple-twist anomalous dimensions

Abstract

Abstract We advance the multipoint lightcone bootstrap and compute anomalous dimensions of triple-twist operators at large spin. In contrast to the well-studied double-twist operators, triple-twist primaries are highly degenerate so that their anomalous dimension is encoded in a matrix. At large spin, the degeneracy becomes infinite and the matrix becomes an integral operator. We compute this integral operator by studying a particular non-planar crossing equation for six-point functions of scalar operators in a lightcone limit. The bootstrap analysis is based on new formulas for six-point lightcone blocks in the comb-channel. For a consistency check of our results, we compare them to perturbative computations in the epsilon expansion of ϕ 3 and ϕ 4 theory. In both cases, we find perfect agreement between perturbative results and bootstrap predictions. As a byproduct of our studies, we complement previous results on triple-twist anomalous dimensions in scalar ϕ 3 and ϕ 4 theory at first and second order in epsilon, respectively.

Keywords

• Scale and Conformal Symmetries
• Renormalization Group
• Space-Time Symmetries