Four-point functions in momentum space: conformal ward identities in the scalar/tensor case
Abstract We derive and analyze the conformal Ward identities (CWI’s) of a tensor 4-point function of a generic CFT in momentum space. The correlator involves the stress–energy tensor T and three scalar operators O (TOOO). We extend the reconstruction method for tensor correlators from 3- to 4-point...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2020-06-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | http://link.springer.com/article/10.1140/epjc/s10052-020-8089-1 |
| _version_ | 1818775534922891264 |
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| author | Claudio Corianò Matteo Maria Maglio Dimosthenis Theofilopoulos |
| author_facet | Claudio Corianò Matteo Maria Maglio Dimosthenis Theofilopoulos |
| author_sort | Claudio Corianò |
| collection | DOAJ |
| description | Abstract We derive and analyze the conformal Ward identities (CWI’s) of a tensor 4-point function of a generic CFT in momentum space. The correlator involves the stress–energy tensor T and three scalar operators O (TOOO). We extend the reconstruction method for tensor correlators from 3- to 4-point functions, starting from the transverse traceless sector of the TOOO. We derive the structure of the corresponding CWI’s in two different sets of variables, relevant for the analysis of the 1–3 (1 graviton $$\rightarrow $$ → 3 scalars) and 2–2 (graviton + scalar $$\rightarrow $$ → two scalars) scattering processes. The equations are all expressed in terms of a single form factor. In both cases we discuss the structure of the equations and their possible behaviors in various asymptotic limits of the external invariants. A comparative analysis of the systems of equations for the TOOO and those for the OOOO, both in the general (conformal) and dual-conformal/conformal (dcc) cases, is presented. We show that in all the cases the Lauricella functions are homogeneous solutions of such systems of equations, also described as parametric 4K integrals of modified Bessel functions. |
| first_indexed | 2024-12-18T10:58:34Z |
| format | Article |
| id | doaj.art-efab131858c14633912cea9265bb1c18 |
| institution | Directory Open Access Journal |
| issn | 1434-6044 1434-6052 |
| language | English |
| last_indexed | 2024-12-18T10:58:34Z |
| publishDate | 2020-06-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-efab131858c14633912cea9265bb1c182022-12-21T21:10:17ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60441434-60522020-06-0180612810.1140/epjc/s10052-020-8089-1Four-point functions in momentum space: conformal ward identities in the scalar/tensor caseClaudio Corianò0Matteo Maria Maglio1Dimosthenis Theofilopoulos2Dipartimento di Matematica e Fisica, Università del Salento and INFN Sezione di LecceDipartimento di Matematica e Fisica, Università del Salento and INFN Sezione di LecceDipartimento di Matematica e Fisica, Università del Salento and INFN Sezione di LecceAbstract We derive and analyze the conformal Ward identities (CWI’s) of a tensor 4-point function of a generic CFT in momentum space. The correlator involves the stress–energy tensor T and three scalar operators O (TOOO). We extend the reconstruction method for tensor correlators from 3- to 4-point functions, starting from the transverse traceless sector of the TOOO. We derive the structure of the corresponding CWI’s in two different sets of variables, relevant for the analysis of the 1–3 (1 graviton $$\rightarrow $$ → 3 scalars) and 2–2 (graviton + scalar $$\rightarrow $$ → two scalars) scattering processes. The equations are all expressed in terms of a single form factor. In both cases we discuss the structure of the equations and their possible behaviors in various asymptotic limits of the external invariants. A comparative analysis of the systems of equations for the TOOO and those for the OOOO, both in the general (conformal) and dual-conformal/conformal (dcc) cases, is presented. We show that in all the cases the Lauricella functions are homogeneous solutions of such systems of equations, also described as parametric 4K integrals of modified Bessel functions.http://link.springer.com/article/10.1140/epjc/s10052-020-8089-1 |
| spellingShingle | Claudio Corianò Matteo Maria Maglio Dimosthenis Theofilopoulos Four-point functions in momentum space: conformal ward identities in the scalar/tensor case European Physical Journal C: Particles and Fields |
| title | Four-point functions in momentum space: conformal ward identities in the scalar/tensor case |
| title_full | Four-point functions in momentum space: conformal ward identities in the scalar/tensor case |
| title_fullStr | Four-point functions in momentum space: conformal ward identities in the scalar/tensor case |
| title_full_unstemmed | Four-point functions in momentum space: conformal ward identities in the scalar/tensor case |
| title_short | Four-point functions in momentum space: conformal ward identities in the scalar/tensor case |
| title_sort | four point functions in momentum space conformal ward identities in the scalar tensor case |
| url | http://link.springer.com/article/10.1140/epjc/s10052-020-8089-1 |
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