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Previous issue date: 2015-05-22 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior - CAPES / A equa??o de Einstein com constante cosmol?gica negativa gera um espa?o-tempo
d + 1?dimens?es, que denominamos de espa?o anti de Sitter, AdSd+1, que nos referimos
de "bulk". O principio hologr?fico afirma que a gravidade qu?ntica sobre o AdSd+1 ? codificada
por uma teoria de contorno, uma CFTd. Por exemplo, uma teoria de cordas IIB
sobre uma espa?o-tempo assintoticamente AdS5 ? S
5
? dual a uma teoria de gauge de
super Yang-Mills N = 4 SYM no espa?o-tempo de 4?dimens?es. Outro exemplo ? a rela-
??o entre a equa??o de Einstein no "bulk"e a equa??o hidrodin?mica descreve uma teoria
efetiva no contorno, o qual denominamos de fluido/gravita??o.
Uma extens?o da dualidadeAdS/CFT foi proposta por Takayanagi que denominou
de correspond?ncia AdS/BCFT. O contorno do CFT extende-se para o "bulk"e restringe
o AdSd+1. Quando impomos a condi??o de Neumann sobre a extens?o do contorno
obtemos uma equa??o de movimento din?mica que determina a forma da extens?o.
Da perspectiva da correspond?ncia fluido/gravita??o o tensor energia-momento do
fluido residindo no contorno ser? a fonte da geometria do "bulk". Ampliando a proposta
de Takayanagi para correspond?ncia fluido/gravita??o estudaremos a consist?ncia
do AdS/BCFT a temperatura finita ou equivalentemente a geometria de BH no "bulk". / Einstein?s equations with negative cosmological constant possess the so-called anti de Sitter
space, AdSd+1, as one of its solutions. We will later refer to this space as to the "bulk".
The holographic principle states that quantum gravity in the AdSd+1 space can be encoded
by a d?dimensional quantum field theory on the boundary of AdSd+1 space, invariant under
conformal transformations, a CFTd. In the most famous example, the precise statement
is the duality of the type IIB string theory in the space AdS5 ? S
5 and the 4?dimensional
N = 4 supersymmetric Yang-Mills theory. Another example is provided by a relation
between Einstein?s equations in the bulk and hydrodynamic equations describing the effective
theory on the boundary, the so-called fluid/gravity correspondence.
An extension of the "AdS/CFT duality"for the CFT?s with boundary was proposed
by Takayanagi, which was dubbed the AdS/BCFT correspondence. The boundary of
a CFT extends to the bulk and restricts a region of the AdSd+1. Neumann conditions imposed
on the extension of the boundary yield a dynamic equation that determines the shape
of the extension. From the perspective of fluid/gravity correspondence, the shape of the
Neumann boundary, and the geometry of the bulk is sourced by the energy-momentum
tensor T?? of a fluid residing on this boundary. Clarifying the relation of the Takayanagi?s
proposal to the fluid/gravity correspondence, we will study the consistence of the
AdS/BCFT with finite temperature CFT?s, or equivalently black hole geometries in the
bulk.
| Identifer | oai:union.ndltd.org:IBICT/oai:repositorio.ufrn.br:123456789/20103 |
| Date | 22 May 2015 |
| Creators | Silva, Madson Rubem Oliveira |
| Contributors | 70183984102, http://lattes.cnpq.br/1078982414439134, Ferraz Filho, ?lvaro, 08158428487, http://lattes.cnpq.br/1699997982151255, Santos, Janilo, 01999044487, http://lattes.cnpq.br/0164449213607380, Sodano, Pasquale, 70080368417, http://lattes.cnpq.br/8680751657359596, Brito, Francisco de Assis de, 75992752404, http://lattes.cnpq.br/4294161599213457, Sifuentes, Rodolfo Alvan Casana, 05159396764, http://lattes.cnpq.br/6508618435773438, Melnikov, Dmitry |
| Publisher | Universidade Federal do Rio Grande do Norte, PROGRAMA DE P?S-GRADUA??O EM F?SICA, UFRN, Brasil |
| Source Sets | IBICT Brazilian ETDs |
| Language | Portuguese |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, info:eu-repo/semantics/doctoralThesis |
| Source | reponame:Repositório Institucional da UFRN, instname:Universidade Federal do Rio Grande do Norte, instacron:UFRN |
| Rights | info:eu-repo/semantics/openAccess |
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