CFT correlators and CP-violating trace anomalies
Abstract We analyze the parity-odd correlators $$\langle JJO\rangle _{odd},$$ ⟨ J J O ⟩ odd , $$\langle JJT\rangle _{odd},$$ ⟨ J J T ⟩ odd , $$\langle TTO\rangle _{odd}$$ ⟨ T T O ⟩ odd and $$\langle TTT\rangle _{odd}$$ ⟨ T T T ⟩ odd in momentum space, constrained by conformal Ward identities, extend...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-09-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-023-11984-z |
| _version_ | 1797647231363317760 |
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| author | Claudio Corianò Stefano Lionetti Matteo Maria Maglio |
| author_facet | Claudio Corianò Stefano Lionetti Matteo Maria Maglio |
| author_sort | Claudio Corianò |
| collection | DOAJ |
| description | Abstract We analyze the parity-odd correlators $$\langle JJO\rangle _{odd},$$ ⟨ J J O ⟩ odd , $$\langle JJT\rangle _{odd},$$ ⟨ J J T ⟩ odd , $$\langle TTO\rangle _{odd}$$ ⟨ T T O ⟩ odd and $$\langle TTT\rangle _{odd}$$ ⟨ T T T ⟩ odd in momentum space, constrained by conformal Ward identities, extending our former investigation of the parity-odd chiral anomaly vertex. We investigate how the presence of parity-odd trace anomalies affect such correlators. Motivations for this study come from holography, early universe cosmology and from a recent debate on the chiral trace anomaly of a Weyl fermion. In the current CFT analysis, O can be either a scalar or a pseudoscalar operator and it can be identified with the trace of the stress–energy tensor. We find that the $$\langle JJO\rangle _{odd}$$ ⟨ J J O ⟩ odd and $$\langle TTO\rangle _{odd}$$ ⟨ T T O ⟩ odd can be different from zero in a CFT. This occurs when the conformal dimension of the scalar operator is $$\Delta _3=4,$$ Δ 3 = 4 , as in the case of $$O=T^{\mu }_{\mu }.$$ O = T μ μ . Moreover, if we assume the existence of parity-odd trace anomalies, the conformal $$\langle JJT\rangle _{odd}$$ ⟨ J J T ⟩ odd and $$\langle TTT\rangle _{odd}$$ ⟨ T T T ⟩ odd are nonzero. In particular, in the case of $$\langle JJT\rangle _{odd}$$ ⟨ J J T ⟩ odd the transverse–traceless component is constrained to vanish, and the correlator is determined only by the trace part with the anomaly pole. |
| first_indexed | 2024-03-11T15:14:20Z |
| format | Article |
| id | doaj.art-f71dc877f50f416386031397841dd678 |
| institution | Directory Open Access Journal |
| issn | 1434-6052 |
| language | English |
| last_indexed | 2024-03-11T15:14:20Z |
| publishDate | 2023-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-f71dc877f50f416386031397841dd6782023-10-29T12:33:34ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522023-09-0183912610.1140/epjc/s10052-023-11984-zCFT correlators and CP-violating trace anomaliesClaudio Corianò0Stefano Lionetti1Matteo Maria Maglio2Dipartimento di Matematica e Fisica, Università del Salento and INFN Sezione di LecceDipartimento di Matematica e Fisica, Università del Salento and INFN Sezione di LecceInstitute for Theoretical Physics (ITP), University of HeidelbergAbstract We analyze the parity-odd correlators $$\langle JJO\rangle _{odd},$$ ⟨ J J O ⟩ odd , $$\langle JJT\rangle _{odd},$$ ⟨ J J T ⟩ odd , $$\langle TTO\rangle _{odd}$$ ⟨ T T O ⟩ odd and $$\langle TTT\rangle _{odd}$$ ⟨ T T T ⟩ odd in momentum space, constrained by conformal Ward identities, extending our former investigation of the parity-odd chiral anomaly vertex. We investigate how the presence of parity-odd trace anomalies affect such correlators. Motivations for this study come from holography, early universe cosmology and from a recent debate on the chiral trace anomaly of a Weyl fermion. In the current CFT analysis, O can be either a scalar or a pseudoscalar operator and it can be identified with the trace of the stress–energy tensor. We find that the $$\langle JJO\rangle _{odd}$$ ⟨ J J O ⟩ odd and $$\langle TTO\rangle _{odd}$$ ⟨ T T O ⟩ odd can be different from zero in a CFT. This occurs when the conformal dimension of the scalar operator is $$\Delta _3=4,$$ Δ 3 = 4 , as in the case of $$O=T^{\mu }_{\mu }.$$ O = T μ μ . Moreover, if we assume the existence of parity-odd trace anomalies, the conformal $$\langle JJT\rangle _{odd}$$ ⟨ J J T ⟩ odd and $$\langle TTT\rangle _{odd}$$ ⟨ T T T ⟩ odd are nonzero. In particular, in the case of $$\langle JJT\rangle _{odd}$$ ⟨ J J T ⟩ odd the transverse–traceless component is constrained to vanish, and the correlator is determined only by the trace part with the anomaly pole.https://doi.org/10.1140/epjc/s10052-023-11984-z |
| spellingShingle | Claudio Corianò Stefano Lionetti Matteo Maria Maglio CFT correlators and CP-violating trace anomalies European Physical Journal C: Particles and Fields |
| title | CFT correlators and CP-violating trace anomalies |
| title_full | CFT correlators and CP-violating trace anomalies |
| title_fullStr | CFT correlators and CP-violating trace anomalies |
| title_full_unstemmed | CFT correlators and CP-violating trace anomalies |
| title_short | CFT correlators and CP-violating trace anomalies |
| title_sort | cft correlators and cp violating trace anomalies |
| url | https://doi.org/10.1140/epjc/s10052-023-11984-z |
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