Conformal partial waves in momentum space
The decomposition of 4-point correlation functions into conformal partial waves is a central tool in the study of conformal field theory. We compute these partial waves for scalar operators in Minkowski momentum space, and find a closed-form result valid in arbitrary space-time dimension $d \geq...
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| Format: | Article |
| Language: | English |
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SciPost
2021-04-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.10.4.081 |
| _version_ | 1831688791798054912 |
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| author | Marc Gillioz |
| author_facet | Marc Gillioz |
| author_sort | Marc Gillioz |
| collection | DOAJ |
| description | The decomposition of 4-point correlation functions into conformal partial
waves is a central tool in the study of conformal field theory. We compute
these partial waves for scalar operators in Minkowski momentum space, and find
a closed-form result valid in arbitrary space-time dimension $d \geq 3$
(including non-integer $d$). Each conformal partial wave is expressed as a sum
over ordinary spin partial waves, and the coefficients of this sum factorize
into a product of vertex functions that only depend on the conformal data of
the incoming, respectively outgoing operators. As a simple example, we apply
this conformal partial wave decomposition to the scalar box integral in $d = 4$
dimensions. |
| first_indexed | 2024-12-20T10:34:39Z |
| format | Article |
| id | doaj.art-d32d3602772f4e919a8160dfd2da6d24 |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-12-20T10:34:39Z |
| publishDate | 2021-04-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-d32d3602772f4e919a8160dfd2da6d242022-12-21T19:43:39ZengSciPostSciPost Physics2542-46532021-04-0110408110.21468/SciPostPhys.10.4.081Conformal partial waves in momentum spaceMarc GilliozThe decomposition of 4-point correlation functions into conformal partial waves is a central tool in the study of conformal field theory. We compute these partial waves for scalar operators in Minkowski momentum space, and find a closed-form result valid in arbitrary space-time dimension $d \geq 3$ (including non-integer $d$). Each conformal partial wave is expressed as a sum over ordinary spin partial waves, and the coefficients of this sum factorize into a product of vertex functions that only depend on the conformal data of the incoming, respectively outgoing operators. As a simple example, we apply this conformal partial wave decomposition to the scalar box integral in $d = 4$ dimensions.https://scipost.org/SciPostPhys.10.4.081 |
| spellingShingle | Marc Gillioz Conformal partial waves in momentum space SciPost Physics |
| title | Conformal partial waves in momentum space |
| title_full | Conformal partial waves in momentum space |
| title_fullStr | Conformal partial waves in momentum space |
| title_full_unstemmed | Conformal partial waves in momentum space |
| title_short | Conformal partial waves in momentum space |
| title_sort | conformal partial waves in momentum space |
| url | https://scipost.org/SciPostPhys.10.4.081 |
| work_keys_str_mv | AT marcgillioz conformalpartialwavesinmomentumspace |