Heriot-Watt Mathematics Report Series
HWM05-1, 18 Jan 2005
Isometric Embeddings and Noncommutative Branes in Homogeneous Gravitational Waves
S Halliday and R J Szabo
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 AdS(3)xS(3)
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.
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