Domain wall flow equations and SU(3)xSU(3) structure compactifications

TL;DR

This paper derives generalized flow equations for supersymmetric domain walls in four-dimensional supergravity from type II compactifications on SU(3)xSU(3) structures, linking geometry with supergravity solutions and potential CFT duals.

Contribution

It introduces a pure spinor approach to formulate flow equations for SU(3)xSU(3) structures, extending Hitchin's framework and connecting 4D and 10D supergravity results.

Findings

Flow equations generalize Hitchin's equations for SU(3)xSU(3) structures.

Established a precise match between 4D and 10D supergravity solutions.

Potential applications in constructing gravity duals of Chern-Simons-matter theories.

Abstract

We study supersymmetric domain wall solutions in four dimensions arising from the compactification of type II supergravity on a SU(3)xSU(3) structure manifold. Using a pure spinor approach, we show that the supersymmetry variations can be reinterpreted as a generalisation of the Hitchin flow equations and describe the embedding of a SU(3)xSU(3) structure manifold into a G_2xG_2 structure manifold. We find a precise agreement between the four- and ten-dimensional supergravity results. The flow equations derived here should have applications in constructing the gravity duals of Chern-Simons-matter conformal field theories.