JHEP 07 (2020) 046                         arXiv link

Heavy-light bootstrap from Lorentzian inversion formula

Yue-Zhou Li^*

Physics Department, Tianjin University, No. 135 Yaguan Road, Tianjin, China

* liyuezhou@tju.edu.cn

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→ ∞. 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  ${\left[{\mathcal{<em>O</em>}}_{\mathrm{<em>_H</em>\; ,}}{\mathcal{<em>O</em>}}_{\mathrm{<em>_L</em>}}\right]}_{{\mathrm{<em>_n</em>}}^{\mathrm{_\prime}}_,{\mathrm{<em>_J</em>}}^{\mathrm{_\prime}}}$. 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.