Holographic Renormalization Made Simple:. an example

Physics – Nuclear Physics

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Scientific paper

We present an alternative method to obtain the exact solution of the bulk field equations for a free scalar field in fixed Euclidean AdSd+l with prescribed but arbitrary Dirichlet boundary conditions. We demonstrate that the Dirichlet boundary conditions allow for a reduction of the second order field equations to a first order problem. The approach is meant to highlight the key points underlying the general method we present in [1], which is a simpler version of what is known as `holographic renorinalization' in the context of the AdS/CFT correspondence. The example we discuss here is special in that an exact solution of the bulk field equations can be obtained and hence the full quantum effective action of the boundary theory can be calculated exactly.

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