A second look at N=1 supersymmetric AdS_4 vacua of type IIA supergravity

TL;DR

The paper investigates ${\cal N}=1$ AdS_4 vacua of type IIA supergravity, linking a class found via a four-dimensional effective potential to explicit ten-dimensional compactifications. It shows that the internal space can be nearly-Kähler, exemplified by $AdS_4 \times S^3 \times S^3 / Z_2^3$, with Bianchi identities for $F_2$ saturable with or without sources depending on flux parameters, including the massless case requiring D6-branes. A detailed D6-brane analysis on the $S^3 \times S^3$ quotient yields explicit tadpole-cancellation configurations and a mapping to the four-dimensional brane setup, including a chiral spectrum. The paper also presents a non nearly-Kähler ${\mathbb CP}^3$ example within the same framework, and connects the AdS_4 vacua to M-theory reductions on the squashed S^7, illustrating the range of admissible flux vacua.

Abstract

We show that a class of type IIA vacua recently found within the N=4 effective approach corresponds to compactification on Ads_4 \times S^3 \times S^3/Z_2^3. The results obtained using the effective method completely match the general ten-dimensional analysis for the existence of N=1 warped compactifications on Ads_4 \times M_6. In particular, we verify that the internal metric is nearly-Kahler and that for specific values of the parameters the Bianchi identity of the RR 2-form is fulfilled without sources. For another range of parameters, including the massless case, the Bianchi identity is satisfied when D6-branes are introduced. Solving the tadpole cancellation conditions in D=4 we are able to find examples of appropriate sets of branes. In the second part of this paper we describe how an example with internal space CP^3 but with non nearly-Kahler metric fits into the general analysis of flux vacua.