Dimensional flow in the kappa-deformed spacetime

Abstract

We derive the modified diffusion equations defined on kappa spacetime and, using these, investigate the change in the spectral dimension of kappa spacetime with the probe scale. These deformed diffusion equations are derived by applying Wick's rotation to the κ-deformed Schrödinger equations obtained from different choices of Klein-Gordon equations in the κ-deformed spacetime. Using the solutions of these equations, obtained by perturbative method, we calculate the spectral dimension for different choices of the generalized Laplacian and analyze the dimensional flow in the κ spacetime. In the limit of commutative spacetime, we recover the well-known equality of spectral dimension and topological dimension. We show that the higher-derivative term in the deformed diffusion equations makes the spectral dimension unbounded (from below) at high energies. We show that the finite mass of the probe results in the spectral dimension becoming infinitely negative at low energies also. In all these cases, we have analyzed the effect of finite size of the probe on the spectral dimension.