Four-point functions of gravitons and conserved currents of CFT in momentum space: testing the nonlocal action with the TTJJ
Abstract We present an analysis of the perturbative realization of the TTJJ correlator, with two stress energy tensors and two conserved currents, using free field theory, integrating out conformal sectors in the quantum corrections. This allows to define, around flat space, an exact perturbative ex...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-05-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-023-11472-4 |
| _version_ | 1797789673057157120 |
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| author | Claudio Corianò Matteo Maria Maglio Riccardo Tommasi |
| author_facet | Claudio Corianò Matteo Maria Maglio Riccardo Tommasi |
| author_sort | Claudio Corianò |
| collection | DOAJ |
| description | Abstract We present an analysis of the perturbative realization of the TTJJ correlator, with two stress energy tensors and two conserved currents, using free field theory, integrating out conformal sectors in the quantum corrections. This allows to define, around flat space, an exact perturbative expansion of the complete anomaly effective action – up to 4-point functions – whose predictions can be compared against those of the anomaly induced action. The latter is a variational solution of the conformal anomaly constraint at $$d=4$$ d = 4 in the form of a nonlocal Wess–Zumino action. The renormalization procedure and the degeneracies of the tensor structures of this correlator are discussed, valid for a generic conformal field theory, deriving its anomalous trace Ward identities (WIs). In this application, we also illustrate a general procedure that identifies the minimal number of tensorial structures and corresponding form factors for the TTJJ and any 4-point function. The approach is implemented for three, four and five dimensions, addressing the tensor degeneracies of the expansion in momentum space. We show that the renormalized TTJJ can be split into two contributions, a non anomalous and an anomalous part, each separately conserved. The first satisfies ordinary trace WIs, while the second satisfies anomalous trace WIs. The result of the direct computation is compared against the expression of the same 4-point function derived from the nonlocal anomaly induced action. We show that the prediction for the anomalous part of the TTJJ derived from such action, evaluated in two different conformal decompositions, the Riegert and Fradkin–Vilkovisky (FV) choices, differ from the anomaly part identified in the perturbative TTJJ, in the flat spacetime limit. The anomaly part of the correlator computed with the Riegert choice is affected by double poles, while the one computed with the FV choice does not satisfy the conservation WIs. We present the correct form of the expansion of the anomaly induced action at the second order in the metric perturbations around flat space that reproduces the perturbative result. |
| first_indexed | 2024-03-13T01:54:01Z |
| format | Article |
| id | doaj.art-f3cc754599c24aa2a01915d980b1c3ef |
| institution | Directory Open Access Journal |
| issn | 1434-6052 |
| language | English |
| last_indexed | 2024-03-13T01:54:01Z |
| publishDate | 2023-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-f3cc754599c24aa2a01915d980b1c3ef2023-07-02T11:24:13ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522023-05-0183513410.1140/epjc/s10052-023-11472-4Four-point functions of gravitons and conserved currents of CFT in momentum space: testing the nonlocal action with the TTJJClaudio Corianò0Matteo Maria Maglio1Riccardo Tommasi2Dipartimento di Matematica e Fisica, Università del Salento and INFN Sezione di LecceInstitute for Theoretical Physics (ITP), University of HeidelbergDipartimento di Matematica e Fisica, Università del Salento and INFN Sezione di LecceAbstract We present an analysis of the perturbative realization of the TTJJ correlator, with two stress energy tensors and two conserved currents, using free field theory, integrating out conformal sectors in the quantum corrections. This allows to define, around flat space, an exact perturbative expansion of the complete anomaly effective action – up to 4-point functions – whose predictions can be compared against those of the anomaly induced action. The latter is a variational solution of the conformal anomaly constraint at $$d=4$$ d = 4 in the form of a nonlocal Wess–Zumino action. The renormalization procedure and the degeneracies of the tensor structures of this correlator are discussed, valid for a generic conformal field theory, deriving its anomalous trace Ward identities (WIs). In this application, we also illustrate a general procedure that identifies the minimal number of tensorial structures and corresponding form factors for the TTJJ and any 4-point function. The approach is implemented for three, four and five dimensions, addressing the tensor degeneracies of the expansion in momentum space. We show that the renormalized TTJJ can be split into two contributions, a non anomalous and an anomalous part, each separately conserved. The first satisfies ordinary trace WIs, while the second satisfies anomalous trace WIs. The result of the direct computation is compared against the expression of the same 4-point function derived from the nonlocal anomaly induced action. We show that the prediction for the anomalous part of the TTJJ derived from such action, evaluated in two different conformal decompositions, the Riegert and Fradkin–Vilkovisky (FV) choices, differ from the anomaly part identified in the perturbative TTJJ, in the flat spacetime limit. The anomaly part of the correlator computed with the Riegert choice is affected by double poles, while the one computed with the FV choice does not satisfy the conservation WIs. We present the correct form of the expansion of the anomaly induced action at the second order in the metric perturbations around flat space that reproduces the perturbative result.https://doi.org/10.1140/epjc/s10052-023-11472-4 |
| spellingShingle | Claudio Corianò Matteo Maria Maglio Riccardo Tommasi Four-point functions of gravitons and conserved currents of CFT in momentum space: testing the nonlocal action with the TTJJ European Physical Journal C: Particles and Fields |
| title | Four-point functions of gravitons and conserved currents of CFT in momentum space: testing the nonlocal action with the TTJJ |
| title_full | Four-point functions of gravitons and conserved currents of CFT in momentum space: testing the nonlocal action with the TTJJ |
| title_fullStr | Four-point functions of gravitons and conserved currents of CFT in momentum space: testing the nonlocal action with the TTJJ |
| title_full_unstemmed | Four-point functions of gravitons and conserved currents of CFT in momentum space: testing the nonlocal action with the TTJJ |
| title_short | Four-point functions of gravitons and conserved currents of CFT in momentum space: testing the nonlocal action with the TTJJ |
| title_sort | four point functions of gravitons and conserved currents of cft in momentum space testing the nonlocal action with the ttjj |
| url | https://doi.org/10.1140/epjc/s10052-023-11472-4 |
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