Liouville Equation in 1/8 BPS Geometries

TL;DR

This paper derives a new differential equation governing 1/8 BPS geometries in IIB supergravity, revealing that solutions reduce to a Liouville equation and correspond to near horizon geometries of intersecting D3-branes.

Contribution

It introduces a new differential equation for controlling functions and shows their solutions relate to known D3-brane geometries.

Findings

Derived a new differential equation for supergravity solutions

Reduced special case to a Liouville equation

Connected solutions to intersecting D3-brane geometries

Abstract

We investigate the 1/8 BPS geometries with SU(2) x U(1) x SO(4) x R symmetry in IIB supergravity which were classified by Gava et al, (hep-th/0611065). It is desirable to have a complete set of differential equations imposed on the controlling functions such that they are not only necessary but also sufficient to produce supergravity solutions with those symmetries. We work on this issue and find a new differential equation for the controlling functions. For a special case, we exhaust all the remaining constraints and show that they reduce to one Liouville equation. The solutions of this equation produce geometries which are locally equivalent to the near horizon geometries of intersecting D3-branes.