Comb Channel Lightcone Bootstrap II: Triple-Twist Anomalous Dimensions

Harris, Sebastian; Kaviraj, Apratim; Quintavalle, Lorenzo; Mann, Jeremy A.; Schomerus, Volker

Preprint

PUBDB-2024-00294

Comb Channel Lightcone Bootstrap II: Triple-Twist Anomalous Dimensions

Harris, S.DESY* ; Kaviraj, A.DESY* ; Mann, J. A. ; Quintavalle, L. (Corresponding author)DESY* ; Schomerus, V.DESY*

2024

[10.3204/PUBDB-2024-00294]

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Report No.: DESY-24-012; arXiv:2401.10986

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 $\phi^3$ and $\phi^4$ theory. In both cases, we find perfect agreement between perturbative results and bootstrap predictions. As a byproduct of our studies, we extend earlier work of Derkachov and Manashov to compute the anomalous dimension matrices of all triple-twist primaries in scalar $\phi^3$ and $\phi^4$ theory to first and second order in epsilon, respectively.

Keyword(s): operator, scalar ; n-point function, 6 ; anomalous dimension ; bootstrap ; spin ; crossing ; epsilon expansion