The DBI Action, Higher-derivative Supergravity, and Flattening Inflaton Potentials

TL;DR

The paper addresses how higher-dimensional, stringy corrections modify scalar kinetic terms in open-string moduli and investigates their inflationary consequences. It identifies the DBI-induced, potential-dependent kinetic term and maps it to specific supersymmetric higher-derivative operators, both in global SUSY and in N=1 supergravity. It shows that the corrections flatten large-field potentials, reducing the tensor-to-scalar ratio for monomial models and enabling a consistent supergravity embedding with moduli stabilization considerations. The work provides analytic and qualitative insights into how string-scale physics can influence observable inflationary predictions.

Abstract

In string theory compactifications it is common to find an effective Lagrangian for the scalar fields with a non-canonical kinetic term. We study the effective action of the scalar position moduli of Type II D$p$-branes. In many instances the kinetic terms are in fact modified by a term proportional to the scalar potential itself. This can be linked to the appearance of higher-dimensional supersymmetric operators correcting the Kähler potential. We identify the supersymmetric dimension-eight operators describing the $α'$ corrections captured by the D-brane Dirac-Born-Infeld action. Our analysis then allows an embedding of the D-brane moduli effective action into an $\mathcal N = 1$ supergravity formulation. The effects of the potential-dependent kinetic terms may be very important if one of the scalars is the inflaton, since they lead to a flattening of the scalar potential. We analyze this flattening effect in detail and compute its impact on the CMB observables for single-field inflation with monomial potentials.

Figures (3)

• Figure 1: Feynman diagram that leads to the presence of \ref{['vertex1']} in the effective action.
• Figure 2: $\psi(\varphi)$ for monomial potentials of various powers $n$.
• Figure 3: CMB observables as predicted by the canonically normalized theory, with initial values $n=2$, $n=1$, $n= \frac{2}{3}$, and $n=\frac{2}{3}$. Darker color means larger values of $av_0$. For small $a v_0$ the effect of the additional kinetic term is negligible, while for large $a v_0$ the potential $V(\psi)$ approaches a monomial with power $1$ for $n=2$, $\frac{2}{3}$ for $n=1$, $\frac{1}{2}$ for $n=\frac{2}{3}$, and so on. The two distinct lines correspond to $N_e = 50$ and $N_e = 60$, respectively.