The renormalisation group approach is applied to the study of the short-time critical behaviour of the d-dimensional Ginzburg-Landau model with long-range interaction of the form p σ s p s −p in momentum space. Firstly the system is quenched from a high temperature to the critical temperature and then relaxes to equilibrium within the model A dynamics. The asymptotic scaling laws and the initial slip exponents θ ′ and θ of the order parameter and the response function respectively, are calculated to the second order in ǫ = 2σ − d.

A family of diffeomorphism-invariant Seiberg-Witten deformations of gravity is constructed. In a first step Seiberg-Witten maps for an SOð1; 3Þ gauge symmetry are obtained for constant deformation parameters. This includes maps for the vierbein, the spin connection, and the Einstein-Hilbert Lagrangian. In a second step the vierbein postulate is imposed in normal coordinates and the deformation parameters are identified with the components ðxÞ of a covariantly constant bivector. This procedure gives for the classical action a power series in the bivector components which by construction is diffeomorphism invariant. Explicit contributions up to second order are obtained. For completeness a cosmological constant term is included in the analysis. Covariant constancy of ðxÞ, together with the field equations, imply that, up to second order, only four-dimensional metrics which are direct sums of two two-dimensional metrics are admissible, the two-dimensional curvatures being expressed in terms of . These four-dimensional metrics can be viewed as a family of deformed emergent gravities.

The field equations coupling a Seiberg-Witten electromagnetic field to noncommutative gravity, as described by a formal power series in the noncommutativity parameters , is investigated. A large family of solutions, up to order one in , describing Einstein-Maxwell null pp-waves is obtained. The order-one contributions can be viewed as providing noncommutative corrections to pp-waves. In our solutions, noncommutativity enters the spacetime metric through a conformal factor and is responsible for dilating/contracting the separation between points in the same null surface. The noncommutative corrections to the electromagnetic waves, while preserving the wave null character, include constant polarization, higher harmonic generation, and inhomogeneous susceptibility. As compared to pure noncommutative gravity, the novelty is that nonzero corrections to the metric already occur at order one in .