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On multi-field flows in gravity and holography. (English) Zbl 1395.83013

Summary: We perform a systematic analysis of flow-like solutions in theories of Einstein gravity coupled to multiple scalar fields, which arise as holographic RG flows as well as in the context of cosmological solutions driven by scalars. We use the first order formalism and the superpotential formulation to classify solutions close to generic extrema of the scalar potential, and close to “bounces,” where the flow is inverted in some or all directions and the superpotential becomes multi-valued. Although the superpotential formulation contains a large redundancy, we show how this can be completely lift by suitable regularity conditions. We place the first order formalism in the context of Hamilton-Jacobi theory, where we discuss the possibility of non-gradient flows and their connection to non-separable solutions of the Hamilton-Jacobi equation. We argue that non-gradient flows may be useful in the presence of global symmetries in the scalar sector.

MSC:

83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
81T17 Renormalization group methods applied to problems in quantum field theory
83F05 Relativistic cosmology
70H20 Hamilton-Jacobi equations in mechanics
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