Aspects of holographic induced gravities[HBNI Th101]

Abstract

In recent years, AdS/CFT correspondance as emereged from string theory as one of the most powerful tools to study consistent theories of gravity by relating them to a boundary conformal field theory(CFT). It relates the partition function of the bulk (super)gravity in a locally Anti-deSitter(AdS) background to the generating function of corelators for the boundary CFT. With the boundary values of the fields in the bulk theory coupling as sources to the operators of the boundary CFT. Therefore the boundary conditions impossed on the bulk (super)gravity theory play an important role in determining the properties of the CFT.

The most studied boundary condition were first introduced by Brown & Henneaux wherein they uncovered 2-copies of Virasoro algebra as the asymptotic symmetry algebra of AdS space in dim=3 (AdS_3) with central extension being c=3//2G with the boundary metric held fixed. These boundary conditions were later generalised to different settings of extended super-gravities and massless higher-spins fields (hs) in ADS_3. Here the super-Virasoro extensions and W∞ were obtained as the asymptotic symmetry algebra respectively.

The thesis concerns itself with consistently defining boundary conditions with fluctuating boundary values of the bulk fields and studying its implications in terms of the AdS_3/CFT_2 correspondance. AdS/CFT suggests that the boundary theory must be an Induced Gravity theory. Induced Gravity theories are generally obtained by coupling the CFT to the 2d background metric and integrating over the CFT degrees of freedom, thus obtaining a diffeomorphic invariant theory but which has Weyl anomalies. The thesis shows that the symmetries of such theories match with those of the bulk AdS_3 theories with boundary conditions which do not fix the boundary values of the bulk fields. This is done by first studying such boundary conditions in the pure gravity setting of AdS_3. These boundary conditions are susbsiquently generalised to extended super-gravities and massless hs fields. In each of these cases the asymptotic symmetry algebra of the Kac-Moody type are found for certain boundary conditions which are also the symmetries of certain Induced gravity theories.

The thesis connects the analysis to recent works in similar directions and ends with some conclusions and discussions.