Harmonic functions and gravity localization
Abstract In models with extra dimensions, matter particles can be easily localized to a ‘brane world’, but gravitational attraction tends to spread out in the extra dimensions unless they are small. Strong warping gradients can help localize gravity closer to the brane. In this note we give a mathem...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-09-01
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| Series: | Journal of High Energy Physics |
| Subjects: | |
| Online Access: | https://doi.org/10.1007/JHEP09(2023)127 |
| _version_ | 1797371195473002496 |
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| author | G. Bruno De Luca Nicolò De Ponti Andrea Mondino Alessandro Tomasiello |
| author_facet | G. Bruno De Luca Nicolò De Ponti Andrea Mondino Alessandro Tomasiello |
| author_sort | G. Bruno De Luca |
| collection | DOAJ |
| description | Abstract In models with extra dimensions, matter particles can be easily localized to a ‘brane world’, but gravitational attraction tends to spread out in the extra dimensions unless they are small. Strong warping gradients can help localize gravity closer to the brane. In this note we give a mathematically rigorous proof that the internal wave-function of the massless graviton is constant as an eigenfunction of the weighted Laplacian, and hence is a power of the warping as a bound state in an analogue Schrödinger potential. This holds even in presence of singularities induced by thin branes. We also reassess the status of AdS vacuum solutions where the graviton is massive. We prove a bound on scale separation for such models, as an application of our recent results on KK masses. We also use them to estimate the scale at which gravity is localized, without having to compute the spectrum explicitly. For example, we point out that localization can be obtained at least up to the cosmological scale in string/M-theory solutions with infinite-volume Riemann surfaces; and in a known class of N $$ \mathcal{N} $$ = 4 models, when the number of NS5- and D5-branes is roughly equal. |
| first_indexed | 2024-03-08T18:16:22Z |
| format | Article |
| id | doaj.art-2ab6f87669384ee99afa6fddab9af2b2 |
| institution | Directory Open Access Journal |
| issn | 1029-8479 |
| language | English |
| last_indexed | 2024-03-08T18:16:22Z |
| publishDate | 2023-09-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj.art-2ab6f87669384ee99afa6fddab9af2b22023-12-31T12:08:05ZengSpringerOpenJournal of High Energy Physics1029-84792023-09-012023914110.1007/JHEP09(2023)127Harmonic functions and gravity localizationG. Bruno De Luca0Nicolò De Ponti1Andrea Mondino2Alessandro Tomasiello3Stanford Institute for Theoretical Physics, Stanford UniversityDipartimento di Matematica e Applicazioni, Università di Milano-BicoccaMathematical Institute, University of OxfordDipartimento di Matematica e Applicazioni, Università di Milano-BicoccaAbstract In models with extra dimensions, matter particles can be easily localized to a ‘brane world’, but gravitational attraction tends to spread out in the extra dimensions unless they are small. Strong warping gradients can help localize gravity closer to the brane. In this note we give a mathematically rigorous proof that the internal wave-function of the massless graviton is constant as an eigenfunction of the weighted Laplacian, and hence is a power of the warping as a bound state in an analogue Schrödinger potential. This holds even in presence of singularities induced by thin branes. We also reassess the status of AdS vacuum solutions where the graviton is massive. We prove a bound on scale separation for such models, as an application of our recent results on KK masses. We also use them to estimate the scale at which gravity is localized, without having to compute the spectrum explicitly. For example, we point out that localization can be obtained at least up to the cosmological scale in string/M-theory solutions with infinite-volume Riemann surfaces; and in a known class of N $$ \mathcal{N} $$ = 4 models, when the number of NS5- and D5-branes is roughly equal.https://doi.org/10.1007/JHEP09(2023)127Classical Theories of GravityFlux CompactificationsSpacetime SingularitiesSuperstring Vacua |
| spellingShingle | G. Bruno De Luca Nicolò De Ponti Andrea Mondino Alessandro Tomasiello Harmonic functions and gravity localization Journal of High Energy Physics Classical Theories of Gravity Flux Compactifications Spacetime Singularities Superstring Vacua |
| title | Harmonic functions and gravity localization |
| title_full | Harmonic functions and gravity localization |
| title_fullStr | Harmonic functions and gravity localization |
| title_full_unstemmed | Harmonic functions and gravity localization |
| title_short | Harmonic functions and gravity localization |
| title_sort | harmonic functions and gravity localization |
| topic | Classical Theories of Gravity Flux Compactifications Spacetime Singularities Superstring Vacua |
| url | https://doi.org/10.1007/JHEP09(2023)127 |
| work_keys_str_mv | AT gbrunodeluca harmonicfunctionsandgravitylocalization AT nicolodeponti harmonicfunctionsandgravitylocalization AT andreamondino harmonicfunctionsandgravitylocalization AT alessandrotomasiello harmonicfunctionsandgravitylocalization |