de-Sitter vacua via consistent D-terms

TL;DR

The paper addresses the challenge of obtaining locally stable $dS$ or Minkowski vacua in $N=1$ supergravity derived from string/M-theory flux compactifications while maintaining consistency with D-term contributions. It proposes a mechanism based on a gauged $U(1)$ that combines an axionic shift with an $R$-symmetry, tightly constraining the $F$- and $D$-term parts of the scalar potential. A concrete single-field model with $K = - p \log(S + S^*) + K_0$, $W = W_0 e^{- k S}$, and $f = S$ exhibits locally stable minima with spontaneously broken SUSY and tunable vacuum energy, including small $dS$ or Minkowski vacua when $V_D$ cancels $V_F$. The work clarifies the conditions under which D-terms can uplift AdS regions in a consistent fashion and discusses potential string theory embeddings in flux compactifications, along with generalizations and open questions about the string origin of the required superpotential modifications.

Abstract

We introduce a new mechanism for producing locally stable de-Sitter or Minkowski vacua, with spontaneously broken N=1 supersymmetry and no massless scalars, applicable to superstring and M-theory compactifications with fluxes. We illustrate the mechanism with a simple N=1 supergravity model that provides parametric control on the sign and the size of the vacuum energy. The crucial ingredient is a gauged U(1) that involves both an axionic shift and an R-symmetry, and severely constrains the F- and D-term contributions to the potential.

Figures (1)

• Figure 1: $V$ (solid line), $V_F$ (dashed line) and $V_D$ (dotted line) for $p=1$, $q=0.3$, $e^{G_0}=1/64$ and $k =0.1$.