A $$ \mathcal{A} $$ -theory — A brane world-volume theory with manifest U-duality
Abstract In this paper, the A $$ \mathcal{A} $$ -theory, an extension of F-theory, is described as a fully U-duality covariant brane theory. This theory has some distinguishing features not known from world-sheet models. In particular, seen as a sigma model, both world-volume and target space coordi...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-10-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP10(2023)087 |
| _version_ | 1827370600245493760 |
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| author | Machiko Hatsuda Ondřej Hulík William D. Linch Warren D. Siegel Di Wang Yu-Ping Wang |
| author_facet | Machiko Hatsuda Ondřej Hulík William D. Linch Warren D. Siegel Di Wang Yu-Ping Wang |
| author_sort | Machiko Hatsuda |
| collection | DOAJ |
| description | Abstract In this paper, the A $$ \mathcal{A} $$ -theory, an extension of F-theory, is described as a fully U-duality covariant brane theory. This theory has some distinguishing features not known from world-sheet models. In particular, seen as a sigma model, both world-volume and target space coordinates are specific representations of the same group (the U-duality group). The U-duality group in question is an exceptional group (a split form of the E d series). The structure of this group allows it to encompass both the T-duality group of string theory as well as the general linear symmetry group of M $$ \mathcal{M} $$ -theory. A $$ \mathcal{A} $$ -theory is defined by the current algebras in Hamiltonian formalism, or by world-volume actions in Lagrangian formalism. The spacetime coordinates are selfdual gauge fields on the world-volume, requiring the Gauß law constraints tying the world-volume to spacetime. Solving the Gauß law constraints/the Virasoro constraints gives the world-volume/spacetime sectioning from A $$ \mathcal{A} $$ -theory to T $$ \mathcal{T} $$ -theory/ M $$ \mathcal{M} $$ -theory respectively. The A $$ \mathcal{A} $$ -theory Lagrangian admits extended symmetry which has not been observed previously in the literature, where the background fields include both the spacetime and the world-volume gravitational fields. We also constructed the four-point amplitude of A $$ \mathcal{A} $$ -theory in the low energy limit. The amplitude is written in a way that the U-duality symmetry is manifest, but after solving the section condition, it reduces to the usual four-graviton amplitude. In the previous papers, we have referred to this model as F-theory, however, F-theory initiated by Vafa is now a big branch of string theory as the study of elliptic fibrations, so we refer to these constructions as generalized models of theory for all dimensions with all duality symmetries as A $$ \mathcal{A} $$ -theory. |
| first_indexed | 2024-03-08T10:17:53Z |
| format | Article |
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| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-08T10:17:53Z |
| publishDate | 2023-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-9617b51ee0244dc78d430d1fdf16c26f2024-01-28T12:13:30ZengSpringerOpenJournal of High Energy Physics1029-84792023-10-0120231016610.1007/JHEP10(2023)087A $$ \mathcal{A} $$ -theory — A brane world-volume theory with manifest U-dualityMachiko Hatsuda0Ondřej Hulík1William D. Linch2Warren D. Siegel3Di Wang4Yu-Ping Wang5Department of Radiological Technology, Faculty of Health Science, Juntendo UniversityTheoretische Natuurkunde, Vrije Universiteit BrusselMercersburg AcademyDepartment of Physics, SUNY Stony Brook UniversityDepartment of Physics, SUNY Stony Brook UniversityDepartment of Physics, SUNY Stony Brook UniversityAbstract In this paper, the A $$ \mathcal{A} $$ -theory, an extension of F-theory, is described as a fully U-duality covariant brane theory. This theory has some distinguishing features not known from world-sheet models. In particular, seen as a sigma model, both world-volume and target space coordinates are specific representations of the same group (the U-duality group). The U-duality group in question is an exceptional group (a split form of the E d series). The structure of this group allows it to encompass both the T-duality group of string theory as well as the general linear symmetry group of M $$ \mathcal{M} $$ -theory. A $$ \mathcal{A} $$ -theory is defined by the current algebras in Hamiltonian formalism, or by world-volume actions in Lagrangian formalism. The spacetime coordinates are selfdual gauge fields on the world-volume, requiring the Gauß law constraints tying the world-volume to spacetime. Solving the Gauß law constraints/the Virasoro constraints gives the world-volume/spacetime sectioning from A $$ \mathcal{A} $$ -theory to T $$ \mathcal{T} $$ -theory/ M $$ \mathcal{M} $$ -theory respectively. The A $$ \mathcal{A} $$ -theory Lagrangian admits extended symmetry which has not been observed previously in the literature, where the background fields include both the spacetime and the world-volume gravitational fields. We also constructed the four-point amplitude of A $$ \mathcal{A} $$ -theory in the low energy limit. The amplitude is written in a way that the U-duality symmetry is manifest, but after solving the section condition, it reduces to the usual four-graviton amplitude. In the previous papers, we have referred to this model as F-theory, however, F-theory initiated by Vafa is now a big branch of string theory as the study of elliptic fibrations, so we refer to these constructions as generalized models of theory for all dimensions with all duality symmetries as A $$ \mathcal{A} $$ -theory.https://doi.org/10.1007/JHEP10(2023)087M-TheoryString DualitySupergravity ModelsSuperspaces |
| spellingShingle | Machiko Hatsuda Ondřej Hulík William D. Linch Warren D. Siegel Di Wang Yu-Ping Wang A $$ \mathcal{A} $$ -theory — A brane world-volume theory with manifest U-duality Journal of High Energy Physics M-Theory String Duality Supergravity Models Superspaces |
| title | A $$ \mathcal{A} $$ -theory — A brane world-volume theory with manifest U-duality |
| title_full | A $$ \mathcal{A} $$ -theory — A brane world-volume theory with manifest U-duality |
| title_fullStr | A $$ \mathcal{A} $$ -theory — A brane world-volume theory with manifest U-duality |
| title_full_unstemmed | A $$ \mathcal{A} $$ -theory — A brane world-volume theory with manifest U-duality |
| title_short | A $$ \mathcal{A} $$ -theory — A brane world-volume theory with manifest U-duality |
| title_sort | mathcal a theory a brane world volume theory with manifest u duality |
| topic | M-Theory String Duality Supergravity Models Superspaces |
| url | https://doi.org/10.1007/JHEP10(2023)087 |
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