Heavy-light Bootstrap from Lorentzian Inversion Formula

TL;DR

This paper develops a bootstrap approach for heavy-light four-point functions in conformal field theories using Lorentzian inversion, revealing universal structures and providing explicit OPE coefficients in various dimensions.

Contribution

It introduces an algorithm to extract OPE data for heavy-light correlators via Lorentzian inversion, including explicit results in four, six, eight, and ten dimensions.

Findings

Universal structure of lowest-twist multi-stress-tensor operators.

Explicit OPE coefficients in $d=4$ up to triple-stress-tensor.

Exact OPE coefficients in $d=6,8,10$.

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.