Aspects of univalence in holographic axion models
Abstract Univalent functions are complex, analytic (holomorphic) and injective functions that have been widely discussed in complex analysis. It was recently proposed that the stringent constraints that univalence imposes on the growth of functions combined with sufficient analyticity conditions cou...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-11-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP11(2022)032 |
| _version_ | 1797865734304432128 |
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| author | Matteo Baggioli Sebastian Grieninger Sašo Grozdanov Zhenkang Lu |
| author_facet | Matteo Baggioli Sebastian Grieninger Sašo Grozdanov Zhenkang Lu |
| author_sort | Matteo Baggioli |
| collection | DOAJ |
| description | Abstract Univalent functions are complex, analytic (holomorphic) and injective functions that have been widely discussed in complex analysis. It was recently proposed that the stringent constraints that univalence imposes on the growth of functions combined with sufficient analyticity conditions could be used to derive rigorous lower and upper bounds on hydrodynamic dispersion relation, i.e., on all terms appearing in their convergent series representations. The results are exact bounds on physical quantities such as the diffusivity and the speed of sound. The purpose of this paper is to further explore these ideas, investigate them in concrete holographic examples, and work towards a better intuitive understanding of the role of univalence in physics. More concretely, we study diffusive and sound modes in a family of holographic axion models and offer a set of observations, arguments and tests that support the applicability of univalence methods for bounding physical observables described in terms of effective field theories. Our work provides insight into expected ‘typical’ regions of univalence, comparisons between the tightness of bounds and the corresponding exact values of certain quantities characterising transport, tests of relations between diffusion and bounds that involve chaotic pole-skipping, as well as tests of a condition that implies the conformal bound on the speed of sound and a complementary condition that implies its violation. |
| first_indexed | 2024-04-09T23:12:56Z |
| format | Article |
| id | doaj.art-47a029573fb440bd9516dea6698a1c34 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-04-09T23:12:56Z |
| publishDate | 2022-11-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-47a029573fb440bd9516dea6698a1c342023-03-22T10:15:11ZengSpringerOpenJournal of High Energy Physics1029-84792022-11-0120221113810.1007/JHEP11(2022)032Aspects of univalence in holographic axion modelsMatteo Baggioli0Sebastian Grieninger1Sašo Grozdanov2Zhenkang Lu3Wilczek Quantum Center, School of Physics and Astronomy, Shanghai Jiao Tong UniversityInstituto de Física Teórica UAM/CSICHiggs Centre for Theoretical Physics, University of EdinburghDepartment of Physics and Astronomy, Uppsala UniversityAbstract Univalent functions are complex, analytic (holomorphic) and injective functions that have been widely discussed in complex analysis. It was recently proposed that the stringent constraints that univalence imposes on the growth of functions combined with sufficient analyticity conditions could be used to derive rigorous lower and upper bounds on hydrodynamic dispersion relation, i.e., on all terms appearing in their convergent series representations. The results are exact bounds on physical quantities such as the diffusivity and the speed of sound. The purpose of this paper is to further explore these ideas, investigate them in concrete holographic examples, and work towards a better intuitive understanding of the role of univalence in physics. More concretely, we study diffusive and sound modes in a family of holographic axion models and offer a set of observations, arguments and tests that support the applicability of univalence methods for bounding physical observables described in terms of effective field theories. Our work provides insight into expected ‘typical’ regions of univalence, comparisons between the tightness of bounds and the corresponding exact values of certain quantities characterising transport, tests of relations between diffusion and bounds that involve chaotic pole-skipping, as well as tests of a condition that implies the conformal bound on the speed of sound and a complementary condition that implies its violation.https://doi.org/10.1007/JHEP11(2022)032Holography and HydrodynamicsGauge-Gravity CorrespondenceField Theory Hydrodynamics |
| spellingShingle | Matteo Baggioli Sebastian Grieninger Sašo Grozdanov Zhenkang Lu Aspects of univalence in holographic axion models Journal of High Energy Physics Holography and Hydrodynamics Gauge-Gravity Correspondence Field Theory Hydrodynamics |
| title | Aspects of univalence in holographic axion models |
| title_full | Aspects of univalence in holographic axion models |
| title_fullStr | Aspects of univalence in holographic axion models |
| title_full_unstemmed | Aspects of univalence in holographic axion models |
| title_short | Aspects of univalence in holographic axion models |
| title_sort | aspects of univalence in holographic axion models |
| topic | Holography and Hydrodynamics Gauge-Gravity Correspondence Field Theory Hydrodynamics |
| url | https://doi.org/10.1007/JHEP11(2022)032 |
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