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

TL;DR

This paper reexamines N=1 supersymmetric AdS_4 vacua in type IIA supergravity, confirming their structure via ten-dimensional analysis, and explores specific internal geometries and flux configurations, including nearly-Kahler and non-nearly-Kahler cases.

Contribution

It provides a detailed match between effective four-dimensional and ten-dimensional analyses of N=1 AdS_4 vacua, clarifying internal geometry and flux conditions, and includes new examples with branes and different internal spaces.

Findings

Internal metric is nearly-Kahler for certain parameters.

Bianchi identity satisfied without sources in specific cases.

Examples with D6-branes and non-nearly-Kahler internal space CP^3.

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.