Single versus multifield scalar potentials from string theory

TL;DR

This paper explores the nature of scalar potentials in string theory, emphasizing that most effective theories are multifield with complex implications for cosmology and potential analysis.

Contribution

It systematically demonstrates that string effective theories are predominantly multifield, affecting how scalar potentials are characterized and understood in cosmological contexts.

Findings

Most string effective theories have at least two non-compact scalar fields.

In multifield theories, the potential's flat directions are better characterized by the gradient vector.

Single field bounds are less meaningful in multifield settings, especially for positive potentials.

Abstract

In this work, we investigate the properties of string effective theories with scalar field(s) and a scalar potential. We first claim that in most examples known, such theories are multifield, with at least 2 non-compact field directions; the few counter-examples appear to be very specific and isolated. Such a systematic multifield situation has important implications for cosmology. Characterising properties of the scalar potential $V$ is also more delicate in a multifield setting. We provide several examples of string effective theories with $V>0$, where the latter admits an asymptotically flat direction along an off-shell field trajectory: in other words, there exists a limit $\varphi \rightarrow \infty$ for which $\frac{|\partial_{\varphi} V|}{V} \rightarrow 0$. It is thus meaningless to look for a lower bound to this single field quantity in a multifield setting; the complete gradient $\nabla V$ is then better suited. Restricting to on-shell trajectories, this question remains open, especially when following the steepest descent or more generally a gradient flow evolution. Interestingly, single field statements in multifield theories seem less problematic for $V<0$.