On multi-field flows in gravity and holography

  • Francesco NittiEmail author
  • Leandro Silva Pimenta
  • Danièle A. Steer
Open Access
Regular Article - Theoretical Physics


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.


AdS-CFT Correspondence Gauge-gravity correspondence 


Open Access

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Copyright information

© The Author(s) 2018

Authors and Affiliations

  • Francesco Nitti
    • 1
    Email author
  • Leandro Silva Pimenta
    • 1
  • Danièle A. Steer
    • 1
  1. 1.APC, AstroParticule et Cosmologie, Université Paris Diderot, CNRS/IN2P3, CEA/IRFU, Observatoire de Paris, Sorbonne Paris CitéParis Cedex 13France

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