Noncommutative Field Theory on Homogeneous Gravitational Waves

TL;DR

This paper develops an algebraic framework for time-dependent noncommutative geometry on a six-dimensional gravitational wave background, enabling the construction and analysis of quantum field theories in this setting.

Contribution

It introduces explicit star-products, constructs the Hopf algebra of twisted isometries, and formulates scalar and D-brane worldvolume field theories in a noncommutative pp-wave background.

Findings

Explicit star-products for the noncommutative geometry are derived.

The Hopf algebra of twisted isometries is constructed.

Scalar and D-brane worldvolume field theories are formulated.

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 of the plane wave 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.