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  • Letter
  • Open Access

Holographic derivation of BPZ-type null-state equations in higher dimensional CFTs

Kuo-Wei Huang

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Phys. Rev. D 114, L081902 – Published 5 October, 2026

DOI: https://doi.org/10.1103/5pbb-fbb6

Abstract

A set of linear differential equations was recently put forward as higher-dimensional generalizations of the BPZ null-state equations in two-dimensional conformal field theories (CFTs) at large central charge. In this work, we derive these higher-dimensional equations from gravity, based on the AdS/CFT correspondence. A near-boundary expansion is employed to analyze a light scalar field equation in a black hole background. There is a decoupling mechanism in the bulk perturbative series at certain conformal dimensions, resulting in isolated lower-order equations. We find that the results agree with the previously proposed four-dimensional CFT equations, which capture the resummed contributions from minimal-twist multistress tensor operators. The holographic calculation also allows one to obtain additional CFT differential equations that extend beyond the near-lightcone regime.

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Phys. Rev. D 114, L081902– Published 5 October, 2026
  • Received 31 May 2026
  • Accepted 26 August 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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