Topology Changing Transitions in Bubbling Geometries

TL;DR

This paper investigates topology-changing transitions in bubbling geometries within Type IIB supergravity, revealing their interpretation as time-dependent interpolations between pp-waves and exploring their resolution via dualities and string theory limits.

Contribution

It provides a detailed analysis of elementary topological transitions, their interpretation as time-dependent geometries, and links to two-dimensional Type 0B string theory and singularity resolution.

Findings

Transitions can be decomposed into elementary steps.

Solutions interpolate between asymptotic pp-waves.

Universal features relate to Type 0B string theory.

Abstract

Topological transitions in bubbling half-BPS Type IIB geometries with SO(4) x SO(4) symmetry can be decomposed into a sequence of n elementary transitions. The half-BPS solution that describes the elementary transition is seeded by a phase space distribution of fermions filling two diagonal quadrants. We study the geometry of this solution in some detail. We show that this solution can be interpreted as a time dependent geometry, interpolating between two asymptotic pp-waves in the far past and the far future. The singular solution at the transition can be resolved in two different ways, related by the particle-hole duality in the effective fermion description. Some universal features of the topology change are governed by two-dimensional Type 0B string theory, whose double scaling limit corresponds to the Penrose limit of AdS_5 x S^5 at topological transition. In addition, we present the full class of geometries describing the vicinity of the most general localized classical singularity that can occur in this class of half-BPS bubbling geometries.