Heriot-Watt Mathematics Report Series
HWM06-5, 20 Jan 2006
Noncommutative Field Theory on Homogeneous Gravitational Waves
S Halliday and R J Szabo
Abstract
We describe an algebraic approach to the time-dependent noncommutative
geometry of a six-dimensional Cahen-Wallach pp-wave string background
supported by a constant Neveu-Schwarz flux, and develop a general
formalism to construct and analyse quantum field theories defined
thereon. Various star-products are derived in closed explicit form and
the Hopf algebra of twisted isometries is constructed. Scalar field
theories are defined using explicit forms of derivative operators,
traces and noncommutative frame fields for the geometry, and various
physical features are described. Noncommutative worldvolume field
theories of D-branes in the pp-wave background are also constructed.
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