Integrating out beyond tree level and relativistic superfluids
Abstract We revisit certain subtleties of renormalization that arise when one derives a low-energy effective action by integrating out the heavy fields of a more complete theory. Usually these subtleties are circumvented by matching some physical observables, such as scattering amplitudes, but a mor...
| 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)066 |
| _version_ | 1811273783396270080 |
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| author | Austin Joyce Alberto Nicolis Alessandro Podo Luca Santoni |
| author_facet | Austin Joyce Alberto Nicolis Alessandro Podo Luca Santoni |
| author_sort | Austin Joyce |
| collection | DOAJ |
| description | Abstract We revisit certain subtleties of renormalization that arise when one derives a low-energy effective action by integrating out the heavy fields of a more complete theory. Usually these subtleties are circumvented by matching some physical observables, such as scattering amplitudes, but a more involved procedure is required if one is interested in deriving the effective theory to all orders in the light fields (but still to fixed order in the derivative expansion). As a concrete example, we study the U(1) Goldstone low-energy effective theory that describes the spontaneously broken phase of a ϕ 4 theory for a complex scalar. Working to lowest order in the derivative expansion, but to all orders in the Goldstones, we integrate out the radial mode at one loop and express the low-energy effective action in terms of the renormalized couplings of the UV completion. This yields the one-loop equation of state for the superfluid phase of (complex) ϕ 4. We perform the same analysis for a renormalizable scalar SO(N) theory at finite chemical potential, integrating out the gapped Goldstones as well, and confirm that the effective theory for the gapless Goldstone exhibits no obvious sign of the original SO(N) symmetry. |
| first_indexed | 2024-04-12T23:05:42Z |
| format | Article |
| id | doaj.art-51af1103bf4a4803a1a65b5d6605c03e |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-12T23:05:42Z |
| publishDate | 2022-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-51af1103bf4a4803a1a65b5d6605c03e2022-12-22T03:12:55ZengSpringerOpenJournal of High Energy Physics1029-84792022-09-012022912510.1007/JHEP09(2022)066Integrating out beyond tree level and relativistic superfluidsAustin Joyce0Alberto Nicolis1Alessandro Podo2Luca Santoni3Kavli Institute for Cosmological Physics, Department of Astronomy and Astrophysics, The University of ChicagoCenter for Theoretical Physics and Department of Physics, Columbia UniversityCenter for Theoretical Physics and Department of Physics, Columbia UniversityICTP, International Centre for Theoretical PhysicsAbstract We revisit certain subtleties of renormalization that arise when one derives a low-energy effective action by integrating out the heavy fields of a more complete theory. Usually these subtleties are circumvented by matching some physical observables, such as scattering amplitudes, but a more involved procedure is required if one is interested in deriving the effective theory to all orders in the light fields (but still to fixed order in the derivative expansion). As a concrete example, we study the U(1) Goldstone low-energy effective theory that describes the spontaneously broken phase of a ϕ 4 theory for a complex scalar. Working to lowest order in the derivative expansion, but to all orders in the Goldstones, we integrate out the radial mode at one loop and express the low-energy effective action in terms of the renormalized couplings of the UV completion. This yields the one-loop equation of state for the superfluid phase of (complex) ϕ 4. We perform the same analysis for a renormalizable scalar SO(N) theory at finite chemical potential, integrating out the gapped Goldstones as well, and confirm that the effective theory for the gapless Goldstone exhibits no obvious sign of the original SO(N) symmetry.https://doi.org/10.1007/JHEP09(2022)066Effective Field TheoriesRenormalization GroupGlobal Symmetries |
| spellingShingle | Austin Joyce Alberto Nicolis Alessandro Podo Luca Santoni Integrating out beyond tree level and relativistic superfluids Journal of High Energy Physics Effective Field Theories Renormalization Group Global Symmetries |
| title | Integrating out beyond tree level and relativistic superfluids |
| title_full | Integrating out beyond tree level and relativistic superfluids |
| title_fullStr | Integrating out beyond tree level and relativistic superfluids |
| title_full_unstemmed | Integrating out beyond tree level and relativistic superfluids |
| title_short | Integrating out beyond tree level and relativistic superfluids |
| title_sort | integrating out beyond tree level and relativistic superfluids |
| topic | Effective Field Theories Renormalization Group Global Symmetries |
| url | https://doi.org/10.1007/JHEP09(2022)066 |
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