Metric approach to a T T ¯ $$ \mathrm{T}\overline{\mathrm{T}} $$ -like deformation in arbitrary dimensions
Abstract We consider a one-parameter family of composite fields — bi-linear in the components of the stress-energy tensor — which generalise the T T ¯ $$ \mathrm{T}\overline{\mathrm{T}} $$ operator to arbitrary space-time dimension d ≥ 2. We show that they induce a deformation of the classical actio...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-09-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP09(2022)085 |
| _version_ | 1797995495324385280 |
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| author | Riccardo Conti Jacopo Romano Roberto Tateo |
| author_facet | Riccardo Conti Jacopo Romano Roberto Tateo |
| author_sort | Riccardo Conti |
| collection | DOAJ |
| description | Abstract We consider a one-parameter family of composite fields — bi-linear in the components of the stress-energy tensor — which generalise the T T ¯ $$ \mathrm{T}\overline{\mathrm{T}} $$ operator to arbitrary space-time dimension d ≥ 2. We show that they induce a deformation of the classical action which is equivalent — at the level of the dynamics — to a field-dependent modification of the background metric tensor according to a specific flow equation. Even though the starting point is the flat space, the deformed metric is generally curved for any d > 2, thus implying that the corresponding deformation can not be interpreted as a coordinate transformation. The central part of the paper is devoted to the development of a recursive algorithm to compute the coefficients of the power series expansion of the solution to the metric flow equation. We show that, under some quite restrictive assumptions on the stress-energy tensor, the power series yields an exact solution. Finally, we consider a class of theories in d = 4 whose stress-energy tensor fulfils the assumptions above mentioned, namely the family of abelian gauge theories in d = 4. For such theories, we obtain the exact expression of the deformed metric and the vierbein. In particular, the latter result implies that ModMax theory in a specific curved space is dynamically equivalent to its Born-Infeld-like extension in flat space. We also discuss a dimensional reduction of the latter theories from d = 4 to d = 2 in which an interesting marginal deformation of d = 2 field theories emerges. |
| first_indexed | 2024-04-11T10:01:29Z |
| format | Article |
| id | doaj.art-21b16118b89249148965a8527ee2a6f0 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-11T10:01:29Z |
| publishDate | 2022-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-21b16118b89249148965a8527ee2a6f02022-12-22T04:30:22ZengSpringerOpenJournal of High Energy Physics1029-84792022-09-012022912310.1007/JHEP09(2022)085Metric approach to a T T ¯ $$ \mathrm{T}\overline{\mathrm{T}} $$ -like deformation in arbitrary dimensionsRiccardo Conti0Jacopo Romano1Roberto Tateo2Departamento de Matemática, Faculdade de Ciências da Universidade de LisboaMax Planck Institute for Dynamics and Self-OrganizationDipartimento di Fisica and Arnold-Regge Center, Università di TorinoAbstract We consider a one-parameter family of composite fields — bi-linear in the components of the stress-energy tensor — which generalise the T T ¯ $$ \mathrm{T}\overline{\mathrm{T}} $$ operator to arbitrary space-time dimension d ≥ 2. We show that they induce a deformation of the classical action which is equivalent — at the level of the dynamics — to a field-dependent modification of the background metric tensor according to a specific flow equation. Even though the starting point is the flat space, the deformed metric is generally curved for any d > 2, thus implying that the corresponding deformation can not be interpreted as a coordinate transformation. The central part of the paper is devoted to the development of a recursive algorithm to compute the coefficients of the power series expansion of the solution to the metric flow equation. We show that, under some quite restrictive assumptions on the stress-energy tensor, the power series yields an exact solution. Finally, we consider a class of theories in d = 4 whose stress-energy tensor fulfils the assumptions above mentioned, namely the family of abelian gauge theories in d = 4. For such theories, we obtain the exact expression of the deformed metric and the vierbein. In particular, the latter result implies that ModMax theory in a specific curved space is dynamically equivalent to its Born-Infeld-like extension in flat space. We also discuss a dimensional reduction of the latter theories from d = 4 to d = 2 in which an interesting marginal deformation of d = 2 field theories emerges.https://doi.org/10.1007/JHEP09(2022)085Field Theories in Lower DimensionsIntegrable Field Theories |
| spellingShingle | Riccardo Conti Jacopo Romano Roberto Tateo Metric approach to a T T ¯ $$ \mathrm{T}\overline{\mathrm{T}} $$ -like deformation in arbitrary dimensions Journal of High Energy Physics Field Theories in Lower Dimensions Integrable Field Theories |
| title | Metric approach to a T T ¯ $$ \mathrm{T}\overline{\mathrm{T}} $$ -like deformation in arbitrary dimensions |
| title_full | Metric approach to a T T ¯ $$ \mathrm{T}\overline{\mathrm{T}} $$ -like deformation in arbitrary dimensions |
| title_fullStr | Metric approach to a T T ¯ $$ \mathrm{T}\overline{\mathrm{T}} $$ -like deformation in arbitrary dimensions |
| title_full_unstemmed | Metric approach to a T T ¯ $$ \mathrm{T}\overline{\mathrm{T}} $$ -like deformation in arbitrary dimensions |
| title_short | Metric approach to a T T ¯ $$ \mathrm{T}\overline{\mathrm{T}} $$ -like deformation in arbitrary dimensions |
| title_sort | metric approach to a t t ¯ mathrm t overline mathrm t like deformation in arbitrary dimensions |
| topic | Field Theories in Lower Dimensions Integrable Field Theories |
| url | https://doi.org/10.1007/JHEP09(2022)085 |
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