W3 Ward identities on a torus

Chang, C. C.; Huang, Chao-Shang; Li, Liang-Xin

doi:10.1016/0370-2693(91)90827-d

Cited by 5 publications

(3 citation statements)

References 20 publications

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“…To obtain the correlation functions of the CFTs with TT deformation on a torus, the procedure is similar to the case in which there is only a single T insertion [78,79], where the correlation functions were derived in the operator formalism. Interestingly, the same results were also obtained in path integral language [77].…”

Section: A Correlation Functions In the Tt-deformed Cftsmentioning

confidence: 99%

“…In terms of the perturbative approach, we obtain the correlation functions with TT deformation systematically by using both operator formalism and path integral language following the analysis in Refs. [77][78][79]. In addition, the correlation functions in the CFT with multiple T's andT's insertion also can be obtained, for example, the case with a TTTT insertion.…”

Section: Introductionmentioning

confidence: 99%

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Correlation functions of CFTs on a torus with a TT¯ deformation

Sun

2020

Phys. Rev. D

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In this paper, we investigate the correlation functions of the conformal field theory (CFT) with the TT deformation on a torus in terms of the perturbative CFT approach, which is the extension of the previous investigations on correlation functions defined on a plane. We systematically obtain the first-order correction to the correlation functions of the CFTs with a TT deformation in both operator formalism and path integral language. As a consistency check, we compute the deformed partition function, namely, the zero-point correlation function, up to the first order, which is consistent with results in the literature. Moreover, we obtain a new recursion relation for correlation functions with multiple T's andT's inserted in generic CFTs on a torus. Based on the recursion relations, we study some correlation functions of stress tensors up to the first order under TT deformation.

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Section: A Correlation Functions In the Tt-deformed Cftsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Correlation functions of CFTs on a torus with a TT¯ deformation

Sun

2020

Phys. Rev. D

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“…With the omission of the contact terms, (3.67) and (3.69) agree with the Ward identity in the torus CFT [60][61][62][63] by the Brown-Henneaux central charge relation c = 3 2G [64]. The dual operator O is a primary operator with conformal weights h = h = 1.…”

Section: Jhep05(2024)254mentioning

confidence: 63%

Holographic torus correlators in AdS3 gravity coupled to scalar field

He,

Li,

Zhang

2024

J. High Energ. Phys.

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This paper investigates holographic torus correlators of generic operators at conformal infinity and a finite cutoff within AdS3 gravity coupled with a free scalar field. Using a near-boundary analysis and solving the gravitational boundary value problem, we solve Einstein’s equation and calculate mixed correlators for massless and massive coupled scalar fields. The conformal Ward identity on the torus has been reproduced holographically, which can be regarded as a consistency check. Further, recurrence relations for a specific class of higher-point correlators are derived, validating AdS3/CFT2 with non-trivial boundary topology. While the two-point scalar correlator is accurately computed on the thermal AdS3 saddle, the higher-point correlators associated with scalar and stress tensor operators are explored.

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Global conformal blocks via shadow formalism

Belavin,

Cabezas

2024

J. High Energ. Phys.

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We study 𝔰𝔩2 and 𝔰𝔩3 global conformal blocks on a sphere and a torus, using the shadow formalism. These blocks arise in the context of Virasoro and 𝒲3 conformal field theories in the large central charge limit. In the 𝔰𝔩2 case, we demonstrate that the shadow formalism yields the known expressions in terms of conformal partial waves. Then, we extend this approach to the 𝔰𝔩3 case and show that it allows to build simple integral representations for 𝔰𝔩3 global blocks. We demonstrate this construction on two examples: the four-point block on the sphere and the one-point torus block.

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W3 Ward identities on a torus

Cited by 5 publications

References 20 publications

Correlation functions of CFTs on a torus with a TT¯ deformation

Correlation functions of CFTs on a torus with a TT¯ deformation

Holographic torus correlators in AdS3 gravity coupled to scalar field

Global conformal blocks via shadow formalism

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