Toward null-state equations in d > 2

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 +...

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Published inThe journal of high energy physics Vol. 2023; no. 11; pp. 203 - 24
Main Author Huang, Kuo-Wei
Format Journal Article
LanguageEnglish
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
Online AccessGet full text

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Abstract 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.
AbstractList 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 = −12 ; the corresponding linear ordinary differential equation can be recast into a schematic form x2uxx + 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, x3uxxxy + 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.
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 = $$ -\frac{1}{2} $$ − 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.
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.
Abstract 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 $$ -\frac{1}{2} $$ ; 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.
ArticleNumber 203
Author Huang, Kuo-Wei
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crossref_primary_10_1007_JHEP09_2024_149
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AdS-CFT Correspondence
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SSID ssj0015190
Score 2.4395645
Snippet 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...
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...
Abstract 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...
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SubjectTerms 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
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Title Toward null-state equations in d > 2
URI https://link.springer.com/article/10.1007/JHEP11(2023)203
https://www.proquest.com/docview/2895066369
https://doaj.org/article/9138026497df4c0082dd02e5d739f254
Volume 2023
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