Functional flows for complex effective actions
In the present work we set up a general functional renormalisation group framework for the computation of complex effective actions. For explicit computations we consider both flows of the Wilsonian effective action and the one-particle irreducible (1PI) effective action. The latter is based on an a...
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| Format: | Article |
| Language: | English |
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SciPost
2023-08-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.15.2.074 |
| _version_ | 1827855404424495104 |
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| author | Friederike Ihssen, Jan M. Pawlowski |
| author_facet | Friederike Ihssen, Jan M. Pawlowski |
| author_sort | Friederike Ihssen, Jan M. Pawlowski |
| collection | DOAJ |
| description | In the present work we set up a general functional renormalisation group framework for the computation of complex effective actions. For explicit computations we consider both flows of the Wilsonian effective action and the one-particle irreducible (1PI) effective action. The latter is based on an appropriate definition of a Legendre transform for complex actions, and we show its validity by comparison to exact results in zero dimensions, as well as a comparison to results for the Wilsonian effective action. In the present implementations of the general approaches, the flow of the Wilsonian effective action has a wider range of applicability and we obtain results for the effective potential of complex fields in $\phi^4$-theories from zero up to four dimensions. These results are also compared with results from the 1PI effective action within its range of applicability. The complex effective action also allows us to determine the location of the Lee-Yang zeros for general parameter values. We also discuss the extension of the present results to general theories including QCD. |
| first_indexed | 2024-03-12T11:50:37Z |
| format | Article |
| id | doaj.art-6eed9f5a62154b119443d1599961d753 |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-03-12T11:50:37Z |
| publishDate | 2023-08-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-6eed9f5a62154b119443d1599961d7532023-08-31T08:39:43ZengSciPostSciPost Physics2542-46532023-08-0115207410.21468/SciPostPhys.15.2.074Functional flows for complex effective actionsFriederike Ihssen, Jan M. PawlowskiIn the present work we set up a general functional renormalisation group framework for the computation of complex effective actions. For explicit computations we consider both flows of the Wilsonian effective action and the one-particle irreducible (1PI) effective action. The latter is based on an appropriate definition of a Legendre transform for complex actions, and we show its validity by comparison to exact results in zero dimensions, as well as a comparison to results for the Wilsonian effective action. In the present implementations of the general approaches, the flow of the Wilsonian effective action has a wider range of applicability and we obtain results for the effective potential of complex fields in $\phi^4$-theories from zero up to four dimensions. These results are also compared with results from the 1PI effective action within its range of applicability. The complex effective action also allows us to determine the location of the Lee-Yang zeros for general parameter values. We also discuss the extension of the present results to general theories including QCD.https://scipost.org/SciPostPhys.15.2.074 |
| spellingShingle | Friederike Ihssen, Jan M. Pawlowski Functional flows for complex effective actions SciPost Physics |
| title | Functional flows for complex effective actions |
| title_full | Functional flows for complex effective actions |
| title_fullStr | Functional flows for complex effective actions |
| title_full_unstemmed | Functional flows for complex effective actions |
| title_short | Functional flows for complex effective actions |
| title_sort | functional flows for complex effective actions |
| url | https://scipost.org/SciPostPhys.15.2.074 |
| work_keys_str_mv | AT friederikeihssenjanmpawlowski functionalflowsforcomplexeffectiveactions |