All 1/2 BPS solutions of IIB supergravity with SO(4) x SO(4) isometry

TL;DR

This paper classifies all 1/2 BPS solutions in IIB supergravity with SO(4) x SO(4) symmetry, confirming that aside from known bubbling geometries, only IIB pp-waves exist as additional solutions.

Contribution

It proves that the only additional 1/2 BPS solutions with SO(4) x SO(4) isometry are IIB pp-waves, completing the classification of such geometries.

Findings

All 1/2 BPS geometries with SO(4) x SO(4) symmetry are either bubbling AdS or IIB pp-waves.

No other 1/2 BPS solutions with these symmetries exist beyond the known classes.

The result confirms the completeness of the bubbling geometries in this context.

Abstract

In hep-th/0409174, Lin, Lunin and Maldacena constructed a set of regular 1/2 BPS geometries in IIB theory. These remarkable `bubbling AdS' geometries have a natural interpretation as duals of chiral primary operators with weight Delta=J in N=4 super-Yang Mills theory. Although these geometries have been assumed to be complete, from a purely supergravity point of view, additional 1/2 BPS configurations may potentially exist with a preferred null isometry. We explore this possibility and prove that the only additional class of 1/2 BPS solutions with SO(4) x SO(4) isometry are the familiar IIB pp-waves.