Toward null-state equations in d > 2

• Published in: The journal of high energy physics Vol. 2023; no. 11; pp. 203 - 24
• Main Author: Huang, Kuo-Wei
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 28.11.2023; Springer Nature B.V; SpringerOpen
• Subjects: AdS-CFT Correspondence; Black holes; Classical and Quantum Gravitation; Correlation; Critical phenomena; Elementary Particles; Equations of state; Field Theories in Higher Dimensions; High energy physics; Light; Mathematical analysis; Ordinary differential equations; Partial differential equations; Phase transitions; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Scale and Conformal Symmetries; String Theory; Symmetry; Tensors; Scale and Conformal Symmetries; AdS-CFT Correspondence; Field Theories in Higher Dimensions
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP11(2023)203

A bstract In two-dimensional CFTs with a large central charge, the level-two BPZ equation governs the heavy-light scalar four-point correlator when the light probe scalar has dimension h = − 1 2 ; the corresponding linear ordinary differential equation can be recast into a schematic form x 2 u xx + u = 0. In this paper, we make an observation that in a class of four-dimensional CFTs with a large central charge, the heavy-light scalar correlator in the near-lightcone limit obeys a similar equation, x 3 u xxxy + u = 0, when the light scalar has dimension ∆ = –1. We focus on the multi-stress tensor sector of the theory and also discuss the corresponding equations for the cases with ∆ = –2, –3. The solutions to these linear partial differential equations in higher dimensions are shown, after a suitable change of variables, to reproduce the near-lightcone correlators previously obtained via holography and the conformal bootstrap.