Asymptotic boundary conditions and square integrability in the partition function of AdS gravity
Abstract There has been renewed interest in the path-integral computation of the partition function of AdS3 gravity, both in the metric and Chern-Simons formulations. The one-loop partition function around Euclidean AdS3 turns out to be given by the vacuum character of Virasoro group. This stems fro...
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doaj-91e9a966124e422daa16435e956893222020-11-25T03:28:20ZengSpringerOpenJournal of High Energy Physics1029-84792020-06-012020611010.1007/JHEP06(2020)172Asymptotic boundary conditions and square integrability in the partition function of AdS gravityJoel Acosta0Alan Garbarz1Andrés Goya2Mauricio Leston3Departamento de Matemática-FCEN-UBA & IMAS-CONICET, Ciudad UniversitariaDepartamento de Física-FCEN-UBA & IFIBA-CONICET, Ciudad UniversitariaDepartamento de Física-FCEN-UBA & IFIBA-CONICET, Ciudad UniversitariaInstituto de Astronomía y Física del Espacio (IAFE), Pabellón IAFE-CONICET, Ciudad UniversitariaAbstract There has been renewed interest in the path-integral computation of the partition function of AdS3 gravity, both in the metric and Chern-Simons formulations. The one-loop partition function around Euclidean AdS3 turns out to be given by the vacuum character of Virasoro group. This stems from the work of Brown and Henneaux (BH) who showed that, in AdS3 gravity with sensible asymptotic boundary conditions, an infinite group of (improper) diffeomorphisms arises which acts canonically on phase space as two independent Virasoro symmetries. The gauge group turns out to be composed of so-called “proper” diffeomorphisms which approach the identity at infinity fast enough. However, it is sometimes far from evident to identify where BH boundary conditions enter in the path integral, and much more difficult to see how the improper diffeomorphisms are left out of the gauge group. In particular, in the metric formulation, Giombi, Maloney and Yin obtained the one-loop partition function around thermal AdS3 resorting to the heat kernel method to compute the determinants coming from the path integral. Here we identify how BH boundary conditions follow naturally from the usual requirement of square-integrability of the metric perturbations. Also, and equally relevant, we clarify how the quotient by only proper diffeomorphisms is implemented, promoting the improper diffeomorphisms to symmetries in the path integral. Our strategy is general enough to apply to other approaches where square integrability is assumed. Finally, we show that square integrability implies that the asymptotic symmetries in higher dimensional AdS gravity are just isometries.http://link.springer.com/article/10.1007/JHEP06(2020)172BRST QuantizationField Theories in Lower DimensionsModels of Quantum Gravity |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Joel Acosta Alan Garbarz Andrés Goya Mauricio Leston |
spellingShingle |
Joel Acosta Alan Garbarz Andrés Goya Mauricio Leston Asymptotic boundary conditions and square integrability in the partition function of AdS gravity Journal of High Energy Physics BRST Quantization Field Theories in Lower Dimensions Models of Quantum Gravity |
author_facet |
Joel Acosta Alan Garbarz Andrés Goya Mauricio Leston |
author_sort |
Joel Acosta |
title |
Asymptotic boundary conditions and square integrability in the partition function of AdS gravity |
title_short |
Asymptotic boundary conditions and square integrability in the partition function of AdS gravity |
title_full |
Asymptotic boundary conditions and square integrability in the partition function of AdS gravity |
title_fullStr |
Asymptotic boundary conditions and square integrability in the partition function of AdS gravity |
title_full_unstemmed |
Asymptotic boundary conditions and square integrability in the partition function of AdS gravity |
title_sort |
asymptotic boundary conditions and square integrability in the partition function of ads gravity |
publisher |
SpringerOpen |
series |
Journal of High Energy Physics |
issn |
1029-8479 |
publishDate |
2020-06-01 |
description |
Abstract There has been renewed interest in the path-integral computation of the partition function of AdS3 gravity, both in the metric and Chern-Simons formulations. The one-loop partition function around Euclidean AdS3 turns out to be given by the vacuum character of Virasoro group. This stems from the work of Brown and Henneaux (BH) who showed that, in AdS3 gravity with sensible asymptotic boundary conditions, an infinite group of (improper) diffeomorphisms arises which acts canonically on phase space as two independent Virasoro symmetries. The gauge group turns out to be composed of so-called “proper” diffeomorphisms which approach the identity at infinity fast enough. However, it is sometimes far from evident to identify where BH boundary conditions enter in the path integral, and much more difficult to see how the improper diffeomorphisms are left out of the gauge group. In particular, in the metric formulation, Giombi, Maloney and Yin obtained the one-loop partition function around thermal AdS3 resorting to the heat kernel method to compute the determinants coming from the path integral. Here we identify how BH boundary conditions follow naturally from the usual requirement of square-integrability of the metric perturbations. Also, and equally relevant, we clarify how the quotient by only proper diffeomorphisms is implemented, promoting the improper diffeomorphisms to symmetries in the path integral. Our strategy is general enough to apply to other approaches where square integrability is assumed. Finally, we show that square integrability implies that the asymptotic symmetries in higher dimensional AdS gravity are just isometries. |
topic |
BRST Quantization Field Theories in Lower Dimensions Models of Quantum Gravity |
url |
http://link.springer.com/article/10.1007/JHEP06(2020)172 |
work_keys_str_mv |
AT joelacosta asymptoticboundaryconditionsandsquareintegrabilityinthepartitionfunctionofadsgravity AT alangarbarz asymptoticboundaryconditionsandsquareintegrabilityinthepartitionfunctionofadsgravity AT andresgoya asymptoticboundaryconditionsandsquareintegrabilityinthepartitionfunctionofadsgravity AT mauricioleston asymptoticboundaryconditionsandsquareintegrabilityinthepartitionfunctionofadsgravity |
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1724584893191553024 |