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We advance the multipoint lightcone bootstrap and compute anomalousdimensions of triple-twist operators at large spin. In contrast to thewell-studied double-twist operators, triple-twist primaries are highlydegenerate so that their anomalous dimension is encoded in a matrix. At largespin, the degeneracy becomes infinite and the matrix becomes an integraloperator. We compute this integral operator by studying a particular non-planarcrossing equation for six-point functions of scalar operators in a lightconelimit. The bootstrap analysis is based on new formulas for six-point lightconeblocks in the comb-channel. For a consistency check of our results, we comparethem to perturbative computations in the epsilon expansion of $\phi^3$ and$\phi^4$ theory. In both cases, we find perfect agreement between perturbativeresults and bootstrap predictions. As a byproduct of our studies, we extendearlier work of Derkachov and Manashov to compute the anomalous dimensionmatrices of all triple-twist primaries in scalar $\phi^3$ and $\phi^4$ theoryto first and second order in epsilon, respectively.

Comb Channel Lightcone Bootstrap II: Triple-Twist Anomalous Dimensions