Nonlinear soft mode action for the large-p SYK model
Abstract The physics of the SYK model at low temperatures is dominated by a soft mode governed by the Schwarzian action. In [1] the linearised action was derived from the soft mode contribution to the four-point function, and physical arguments were presented for its nonlinear completion to the Schw...
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SpringerOpen
2025-03-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP03(2025)089 |
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| author | Marta Bucca Márk Mezei |
| author_facet | Marta Bucca Márk Mezei |
| author_sort | Marta Bucca |
| collection | DOAJ |
| description | Abstract The physics of the SYK model at low temperatures is dominated by a soft mode governed by the Schwarzian action. In [1] the linearised action was derived from the soft mode contribution to the four-point function, and physical arguments were presented for its nonlinear completion to the Schwarzian. In this paper, we give two derivations of the full nonlinear effective action in the large p limit, where p is the number of fermions in the interaction terms of the Hamiltonian. The first derivation uses that the collective field action of the large-p SYK model is Liouville theory with a non-conformal boundary condition that we study in conformal perturbation theory. This derivation can be viewed as an explicit version of the renormalisation group argument for the nonlinear soft mode action in [2]. The second derivation uses an Ansatz for how the soft mode embeds into the microscopic configuration space of the collective fields. We generalise our results for the large-p SYK chain and obtain a “Schwarzian chain” effective action for it. These derivations showcase that the large-p SYK model is a rare system, in which there is sufficient control over the microscopic dynamics, so that an effective description can be derived for it without the need for extra assumptions or matching (in the effective field theory sense). |
| format | Article |
| id | doaj-art-4e7e0bea4ad044daafc83cce3a259eb2 |
| institution | DOAJ |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-4e7e0bea4ad044daafc83cce3a259eb22025-08-20T03:06:48ZengSpringerOpenJournal of High Energy Physics1029-84792025-03-012025311910.1007/JHEP03(2025)089Nonlinear soft mode action for the large-p SYK modelMarta Bucca0Márk Mezei1Mathematical Institute, University of OxfordMathematical Institute, University of OxfordAbstract The physics of the SYK model at low temperatures is dominated by a soft mode governed by the Schwarzian action. In [1] the linearised action was derived from the soft mode contribution to the four-point function, and physical arguments were presented for its nonlinear completion to the Schwarzian. In this paper, we give two derivations of the full nonlinear effective action in the large p limit, where p is the number of fermions in the interaction terms of the Hamiltonian. The first derivation uses that the collective field action of the large-p SYK model is Liouville theory with a non-conformal boundary condition that we study in conformal perturbation theory. This derivation can be viewed as an explicit version of the renormalisation group argument for the nonlinear soft mode action in [2]. The second derivation uses an Ansatz for how the soft mode embeds into the microscopic configuration space of the collective fields. We generalise our results for the large-p SYK chain and obtain a “Schwarzian chain” effective action for it. These derivations showcase that the large-p SYK model is a rare system, in which there is sufficient control over the microscopic dynamics, so that an effective description can be derived for it without the need for extra assumptions or matching (in the effective field theory sense).https://doi.org/10.1007/JHEP03(2025)089Field Theories in Lower DimensionsHolography and Condensed Matter Physics (AdS/CMT)Random Systems |
| spellingShingle | Marta Bucca Márk Mezei Nonlinear soft mode action for the large-p SYK model Journal of High Energy Physics Field Theories in Lower Dimensions Holography and Condensed Matter Physics (AdS/CMT) Random Systems |
| title | Nonlinear soft mode action for the large-p SYK model |
| title_full | Nonlinear soft mode action for the large-p SYK model |
| title_fullStr | Nonlinear soft mode action for the large-p SYK model |
| title_full_unstemmed | Nonlinear soft mode action for the large-p SYK model |
| title_short | Nonlinear soft mode action for the large-p SYK model |
| title_sort | nonlinear soft mode action for the large p syk model |
| topic | Field Theories in Lower Dimensions Holography and Condensed Matter Physics (AdS/CMT) Random Systems |
| url | https://doi.org/10.1007/JHEP03(2025)089 |
| work_keys_str_mv | AT martabucca nonlinearsoftmodeactionforthelargepsykmodel AT markmezei nonlinearsoftmodeactionforthelargepsykmodel |