Isometric Embeddings and Noncommutative Branes in Homogeneous Gravitational Waves

TL;DR

This paper characterizes the worldvolume theories on symmetric D-branes in a six-dimensional gravitational wave background, revealing flat and curved noncommutative branes and their relation to string theory limits and spacetime embeddings.

Contribution

It introduces a detailed analysis of noncommutative D-branes in a Cahen-Wallach pp-wave, including flat and curved cases, and connects these to spacetime embeddings and Penrose-Gueven limits.

Findings

Identifies flat noncommutative Euclidean D3-branes analogous to magnetic backgrounds.

Describes curved noncommutative Lorentzian D3-branes similar to electric backgrounds.

Constructs noncommutative field theories from first principles and analyzes their limits.

Abstract

We characterize the worldvolume theories on symmetric D-branes in a six-dimensional Cahen-Wallach pp-wave supported by a constant Neveu-Schwarz three-form flux. We find a class of flat noncommutative euclidean D3-branes analogous to branes in a constant magnetic field, as well as curved noncommutative lorentzian D3-branes analogous to branes in an electric background. In the former case the noncommutative field theory on the branes is constructed from first principles, related to dynamics of fuzzy spheres in the worldvolumes, and used to analyse the flat space limits of the string theory. The worldvolume theories on all other symmetric branes in the background are local field theories. The physical origins of all these theories are described through the interplay between isometric embeddings of branes in the spacetime and the Penrose-Gueven limit of AdS3 x S3 with Neveu-Schwarz three-form flux. The noncommutative field theory of a non-symmetric spacetime-filling D-brane is also constructed, giving a spatially varying but time-independent noncommutativity analogous to that of the Dolan-Nappi model.