Holographic Derivation of BPZ-Type Null State Equations in Higher Dimensional CFTs
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914531881517056 |
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| author | Huang, Kuo-Wei |
| author_facet | Huang, Kuo-Wei |
| contents | A set of linear differential equations was recently put forward as higher-dimensional generalizations of the BPZ null-state equations in two-dimensional 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 multi-stress tensor operators. The holographic calculation also allows one to obtain additional CFT differential equations that extend beyond the near-lightcone regime. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_04032 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Holographic Derivation of BPZ-Type Null State Equations in Higher Dimensional CFTs Huang, Kuo-Wei High Energy Physics - Theory A set of linear differential equations was recently put forward as higher-dimensional generalizations of the BPZ null-state equations in two-dimensional 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 multi-stress tensor operators. The holographic calculation also allows one to obtain additional CFT differential equations that extend beyond the near-lightcone regime. |
| title | Holographic Derivation of BPZ-Type Null State Equations in Higher Dimensional CFTs |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2605.04032 |