On the Ricci flow and emergent quantum mechanics

The Ricci flow equation of a conformally flat Riemannian metric on a closed 2-dimensional configuration space is analysed. It turns out to be equivalent to the classical Hamilton-Jacobi equation for a point particle subject to a potential function that is proportional to the Ricci scalar curvature of configuration space. This allows one to obtain Schroedinger quantum mechanics from Perelman's action functional: the quantum-mechanical wavefunction is the exponential of $i$ times the conformal factor of the metric on configuration space. We explore links with the recently discussed emergent quantum mechanics.Comment: To appear in the proceedings of DICE'08 (Castiglioncello, Italy, Sept. 2008), edited by H.-T. Elz

Spontaneous CP Violation in Non-Minimal Supersymmetric Models

We study the possibilities of spontaneous CP violation in the Next-to-Minimal Supersymmetric Standard Model with an extra singlet tadpole term in the scalar potential. We calculate the Higgs boson masses and couplings with radiative corrections including dominant two loop terms. We show that it is possible to satisfy the LEP constraints on the Higgs boson spectrum with non-trivial spontaneous CP violating phases. We also show that these phases could account for the observed value of epsilonK.Comment: 21 pages, 7 Figures in Encapsulated Postscrip

Quantum gravity and gravitational-wave astronomy

We investigate possible signatures of quantum gravity which could be tested with current and future gravitational-wave (GW) observations. In particular, we analyze how quantum gravity can influence the GW luminosity distance, the time dependence of the effective Planck mass and the instrumental strain noise of interferometers. Using both model-dependent and model-independent formulae, we show that these quantities can encode a non-perturbative effect typical of all quantum-gravity theories, namely the way the dimension of spacetime changes with the probed scale. Effects associated with such dimensional flow might be tested with GW observations and constrained significantly in theories with a microscopically discrete spacetime geometry, more strongly than from propagation-speed constraints. Making use of public LIGO data as well as of a simulated higher-redshift LISA source, we impose the first, respectively, actual and mock constraints on quantum-gravity parameters affecting the GW luminosity distance and discuss specific theoretical examples. If also the Newtonian potential is modified but light geodesics are not, then solar-system bounds may be stronger than GW ones. Yet, for some theories GW astronomy can give unique information not available from solar-system tests