Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2010-09-30
J.Phys.Conf.Ser.283:012004,2011
Physics
High Energy Physics
High Energy Physics - Theory
19 pages, 1 figure, contribution to conference proceedings (NEB14); minor typos corrected in v2
Scientific paper
10.1088/1742-6596/283/1/012004
I provide a broad framework to embed gradient flow equations in non-relativistic field theory models that exhibit anisotropic scaling. The prime example is the heat equation arising from a Lifshitz scalar field theory; other examples include the Allen-Cahn equation that models the evolution of phase boundaries. Then, I review recent results reported in arXiv:1002.0062 describing instantons of Horava-Lifshitz gravity as eternal solutions of certain geometric flow equations on 3-manifolds. These instanton solutions are in general chiral when the anisotropic scaling exponent is z=3. Some general connections with the Onsager-Machlup theory of non-equilibrium processes are also briefly discussed in this context. Thus, theories of Lifshitz type in d+1 dimensions can be used as off-shell toy models for dynamical vacuum selection of relativistic field theories in d dimensions.
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