Holography for asymptotically locally Lifshitz spacetimes. (English) Zbl 1230.83018
Summary: We give a definition of asymptotically locally Lifshitz spacetimes, with boundary data appropriate for a non-relativistic theory on the boundary. Solutions satisfying these boundary conditions are constructed in an asymptotic expansion. We identify the boundary data with sources for dual field theory operators, and give a prescription for calculating the one-point functions of the field theory operators (including the stress tensor) in the presence of arbitrary sources. The divergences in these one-point functions can be cancelled by holographic renormalization, adding counterterms which are local functions of the boundary data.
MSC:
83C05 | Einstein’s equations (general structure, canonical formalism, Cauchy problems) |
83C25 | Approximation procedures, weak fields in general relativity and gravitational theory |
81T15 | Perturbative methods of renormalization applied to problems in quantum field theory |
81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
83C45 | Quantization of the gravitational field |
83D05 | Relativistic gravitational theories other than Einstein’s, including asymmetric field theories |