Heavy-light Bootstrap from Lorentzian Inversion Formula

Abstract

We study heavy-light four-point function by employing Lorentzian inversion formula, where the conformal dimension of heavy operator is as large as central charge $C_T\rightarrow\infty$. We implement the Lorentzian inversion formula back and forth to reveal the universality of the lowest-twist multi-stress-tensor $T^k$ as well as large spin double-twist operators $[\mathcal{O}_H\mathcal{O}_L]_{n',J'}$. In this way, we also propose an algorithm to bootstrap the heavy-light four-point function by extracting relevant OPE coefficients and anomalous dimensions. By following the algorithm, we exhibit the explicit results in $d=4$ up to the triple-stress-tensor. Moreover, general dimensional heavy-light bootstrap up to the double-stress-tensor is also discussed, and we present an infinite series representation of the lowest-twist double-stress-tensor OPE coefficient. Exact expressions of lowest-twist double-stress-tensor OPE coefficients in $d=6,8,10$ are also obtained as further examples.