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| Format: | Preprint |
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2023
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| Online Access: | https://arxiv.org/abs/2308.03229 |
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| _version_ | 1866929428106313728 |
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| author | Huang, Kuo-Wei |
| author_facet | Huang, Kuo-Wei |
| contents | 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 $h= - {1\over 2}$; 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 $Δ=-1$. We focus on the multi-stress tensor sector of the theory and also discuss the corresponding equations for the cases with $Δ= -2, -3$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_03229 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Toward Null State Equations in $d>2$ Huang, Kuo-Wei High Energy Physics - Theory 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 $h= - {1\over 2}$; 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 $Δ=-1$. We focus on the multi-stress tensor sector of the theory and also discuss the corresponding equations for the cases with $Δ= -2, -3$. 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. |
| title | Toward Null State Equations in $d>2$ |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2308.03229 |