On multi-field flows in gravity and holography

TL;DR

This paper systematically analyzes multi-field flow solutions in Einstein gravity with scalar fields, classifying holographic and cosmological flows, and exploring the superpotential formalism and non-gradient flows.

Contribution

It provides a comprehensive classification of multi-field flows near extrema and bounces, and clarifies the superpotential formalism's redundancy and its relation to Hamilton-Jacobi theory.

Findings

Classified solutions near extrema and bounces.

Resolved superpotential formalism redundancy.

Explored non-gradient flows and their relation to symmetries.

Abstract

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.