The Embedding of Superstring Backgrounds in Einstein Gravity

TL;DR

This paper demonstrates how various superstring backgrounds, including those with non-trivial fields, can be embedded into higher-dimensional Ricci-flat Einstein spaces, revealing new geometric connections in string theory.

Contribution

It introduces a theorem for embedding superstring backgrounds with null Killing vectors into eleven-dimensional Ricci-flat spaces, linking supergravity solutions to Einstein gravity.

Findings

Superstring backgrounds with covariantly constant null Killing vectors can be embedded in eleven-dimensional Ricci-flat spaces.

Exact type IIB backgrounds with Ramond-Ramond fields are included in the embedding.

A twelve-dimensional Ricci-flat space embedding of eleven-dimensional supergravity solutions is constructed.

Abstract

A theorem of differential geometry is employed to locally embed a wide class of superstring backgrounds that admit a covariantly constant null Killing vector field in eleven-dimensional, Ricci-flat spaces. Included in this class are exact type IIB superstring backgrounds with non-trivial Ramond-Ramond fields and a class of supersymmetric string waves. The embedding spaces represent exact solutions to eleven-dimensional, vacuum Einstein gravity. A solution of eleven-dimensional supergravity is also embedded in a twelve--dimensional, Ricci-flat space.