Single versus multifield scalar potentials from string theory

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 \(\widehat{\varphi }\to \infty \) for which \(\frac{\left|{\partial }_{\widehat{\varphi }}V\right|}{V}\to 0\). It is thus meaningless to look for a lower bound to this single field quantity in a multifield setting; the complete gradient ∇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.