Approximate symmetries in d = 4 CFTs with an Einstein gravity dual

• Published in: The journal of high energy physics Vol. 2022; no. 9; pp. 53 - 15
• Main Author: Huang, Kuo-Wei
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 06.09.2022; Springer Nature B.V; Springer Nature; SpringerOpen
• Subjects: Algebra; Classical and Quantum Gravitation; CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Conformal and W Symmetry; Elementary Particles; Field Theories in Higher Dimensions; Gravity; High energy physics; Mathematical analysis; Operators (mathematics); Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; Statistical methods; String Theory; Symmetry; Tensors; Field Theories in Higher Dimensions; Conformal and W Symmetry
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP09(2022)053

A bstract By applying the stress-tensor-scalar operator product expansion (OPE) twice, we search for algebraic structures in d = 4 conformal field theories (CFTs) with a pure Einstein gravity dual. We find that a rescaled mode operator defined by an integral of the stress tensor T ++ on a d = 2 plane satisfies a Virasoro-like algebra when the dimension of the scalar is large. The structure is enhanced to include a Kac-Moody-type algebra if we incorporate the T −− component. In our scheme, the central terms are finite. It remains challenging to directly compute the stress-tensor sector of d = 4 scalar four-point functions at large central charge, which, based on holography and bootstrap methods, were recently shown to have a Virasoro/ W -algebra vacuum block-like structure.