On the coupling of Galilean-invariant field theories to curved spacetime
We consider the problem of coupling Galilean-invariant quantum field theories to a fixed spacetime. We propose that to do so, one couples to Newton-Cartan geometry and in addition imposes a one-form shift symmetry. This additional symmetry imposes invariance under Galilean boosts, and its Ward id...
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| Format: | Article |
| Language: | English |
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SciPost
2018-07-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.5.1.011 |
| _version_ | 1819298205646454784 |
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| author | Kristan Jensen |
| author_facet | Kristan Jensen |
| author_sort | Kristan Jensen |
| collection | DOAJ |
| description | We consider the problem of coupling Galilean-invariant quantum field theories
to a fixed spacetime. We propose that to do so, one couples to Newton-Cartan
geometry and in addition imposes a one-form shift symmetry. This additional
symmetry imposes invariance under Galilean boosts, and its Ward identity
equates particle number and momentum currents. We show that Newton-Cartan
geometry subject to the shift symmetry arises in null reductions of Lorentzian
manifolds, and so our proposal is realized for theories which are
holographically dual to quantum gravity on Schr\"odinger spacetimes. We use
this null reduction to efficiently form tensorial invariants under the boost
and particle number symmetries. We also explore the coupling of
Schr\"odinger-invariant field theories to spacetime, which we argue
necessitates the Newton-Cartan analogue of Weyl invariance. |
| first_indexed | 2024-12-24T05:26:12Z |
| format | Article |
| id | doaj.art-431c68cccb9046dcbcb2d7534558a06a |
| institution | Directory Open Access Journal |
| issn | 2542-4653 |
| language | English |
| last_indexed | 2024-12-24T05:26:12Z |
| publishDate | 2018-07-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj.art-431c68cccb9046dcbcb2d7534558a06a2022-12-21T17:13:19ZengSciPostSciPost Physics2542-46532018-07-015101110.21468/SciPostPhys.5.1.011On the coupling of Galilean-invariant field theories to curved spacetimeKristan JensenWe consider the problem of coupling Galilean-invariant quantum field theories to a fixed spacetime. We propose that to do so, one couples to Newton-Cartan geometry and in addition imposes a one-form shift symmetry. This additional symmetry imposes invariance under Galilean boosts, and its Ward identity equates particle number and momentum currents. We show that Newton-Cartan geometry subject to the shift symmetry arises in null reductions of Lorentzian manifolds, and so our proposal is realized for theories which are holographically dual to quantum gravity on Schr\"odinger spacetimes. We use this null reduction to efficiently form tensorial invariants under the boost and particle number symmetries. We also explore the coupling of Schr\"odinger-invariant field theories to spacetime, which we argue necessitates the Newton-Cartan analogue of Weyl invariance.https://scipost.org/SciPostPhys.5.1.011 |
| spellingShingle | Kristan Jensen On the coupling of Galilean-invariant field theories to curved spacetime SciPost Physics |
| title | On the coupling of Galilean-invariant field theories to curved spacetime |
| title_full | On the coupling of Galilean-invariant field theories to curved spacetime |
| title_fullStr | On the coupling of Galilean-invariant field theories to curved spacetime |
| title_full_unstemmed | On the coupling of Galilean-invariant field theories to curved spacetime |
| title_short | On the coupling of Galilean-invariant field theories to curved spacetime |
| title_sort | on the coupling of galilean invariant field theories to curved spacetime |
| url | https://scipost.org/SciPostPhys.5.1.011 |
| work_keys_str_mv | AT kristanjensen onthecouplingofgalileaninvariantfieldtheoriestocurvedspacetime |