Abstract
We consider a holographic dual model for defect conformal field theories (DCFT) in which we include the backreaction of the defect on the dual geometry. In particular, we consider a dual gravity system in which a two-dimensional hypersurface with matter fields, the brane, is embedded into a three-dimensional asymptotically Anti-de Sitter spacetime. Motivated by recent proposals for holographic duals of boundary conformal field theories (BCFT), we assume the geometry of the brane to be determined by Israel junction conditions. We show that these conditions are intimately related to the energy conditions for the brane matter fields, and explain how these energy conditions constrain the possible geometries. This has implications for the holographic entanglement entropy in particular. Moreover, we give exact analytical solutions for the case where the matter content of the brane is a perfect fluid, which in a particular case corresponds to a free massless scalar field. Finally, we describe how our results may be particularly useful for extending a recent proposal for a holographic Kondo model.
Highlights
There are important examples of physical systems which contain degrees of freedom confined to a lower-dimensional subspace of spacetime and can be described by conformal field theories
We find a connection between the assumption made for this theorem and a specific combination of energy conditions, which can be used to distinguish between hypersurface configurations which are anchored twice at the boundary, and others which are infinitely extended into the bulk
The major motivation to investigate the backreaction on the geometry is that it is necessary for calculating the entanglement entropy using the Ryu-Takayanagi proposal [35, 36]
Summary
There are important examples of physical systems which contain degrees of freedom confined to a lower-dimensional subspace of spacetime and can be described by conformal field theories. In the AdS/BCFT models mentioned above [18,19,20], von Neumann boundary conditions are imposed on the brane and, as usual, Dirichlet conditions on the conformal boundary This ansatz yields the same equations of motion as the use of Israel junction conditions. According to the result of this present paper, the Israel junction conditions are the natural choice to describe the backreaction that the energy-momentum localised on the brane exerts on the overall geometry This allows for the calculation of the HEE in AdS/BCFT, as was already done in [15], and in AdS/DCFT models such as in [30].
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