On multi-field flows in gravity and holography
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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.
KeywordsAdS-CFT Correspondence Gauge-gravity correspondence
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- W. Boucher, Positive energy without supersymmetry, Nucl. Phys. B 242 (1984) 282 [INSPIRE].
- P.K. Townsend, Positive energy and the scalar potential in higher dimensional (super)gravity theories, Phys. Lett. B 148 (1984) 55.Google Scholar
- I. Papadimitriou, Lectures on holographic renormalization, Springer Proc. Phys. 176 (2016) 131.Google Scholar
- D.S. Salopek and J.R. Bond, Nonlinear evolution of long wavelength metric fluctuations in inflationary models, Phys. Rev. D 42 (1990) 3936 [INSPIRE].
- T. Banks and L.J. Dixon, Constraints on string vacua with space-time supersymmetry, Nucl. Phys. B 307 (1988) 93 [INSPIRE].