Effective action of (massive) IIA on manifolds with SU(3) structure

TL;DR

This work demonstrates that Romans' massive type IIA supergravity compactified on SU(3) structure manifolds can generate a nonperturbatively stabilised moduli sector without orientifolds or nonperturbative effects. By reducing the fermionic sector, the authors derive the ${\cal N}=2$ gravitino mass matrix and show that vevs of internal fields lead to spontaneous partial supersymmetry breaking ${\cal N}=2\to{\cal N}=1$, with the surviving fields forming an ${\cal N}=1$ effective theory characterized by a holomorphic superpotential $W$ and a Kähler potential $K$. They provide explicit expressions for $W$ and $K$ in general and in a concrete coset example ${SU(3)}/{U(1)\times U(1)}$, where all geometric and axio-dilaton moduli are stabilised at nontrivial values in an AdS vacuum, independent of nonperturbative dynamics. The results offer a concrete moduli-stabilisation mechanism within a controlled geometric framework and suggest avenues for exploring similar breaking patterns and vacua on other SU(3) structure manifolds. The findings have potential implications for phenomenology and for constructing explicit four-dimensional theories from string/M-theory compactifications.

Abstract

In this paper we consider compactifications of massive type IIA supergravity on manifolds with SU(3) structure. We derive the gravitino mass matrix of the effective four-dimensional N = 2 theory and show that vacuum expectation values of the scalar fields naturally induce spontaneous partial supersymmetry breaking. We go on to derive the superpotential and the Kaehler potential for the resulting N = 1 theories. As an example we consider the SU(3) structure manifold SU(3)/U(1)xU(1) and explicitly find N = 1 supersymmetric minima where all the moduli are stabilised at non-trivial values without the use of non-perturbative effects.

Figures (2)

• Figure 1: Plot showing the scalar potential for the directions $\xi^0$ and $e^{-\phi}$ (denoted as $D$).
• Figure 2: Plot showing the scalar potential for the directions $\widetilde{b}$ and $\widetilde{v}$.