Heat kernel expansion and induced action for matrix models

In this proceeding note, I review some recent results concerning the quantum effective action of certain matrix models, i.e. the supersymmetric IKKT model, in the context of emergent gravity. The absence of pathological UV/IR mixing is discussed, as well as dynamical SUSY breaking and some relations with string theory and supergravity.Comment: 11 pages, 1 figure; talk given at the 7th International Conference on Quantum Theory and Symmetries, August 7-13, 2011, Prague/Czech Republi

Phase diagrams in nonlocal PNJL models constrained by Lattice QCD results

Based on lattice QCD-adjusted SU(2) nonlocal Polyakov--Nambu--Jona-Lasinio (PNJL) models, we investigate how the location of the critical endpoint in the QCD phase diagram depends on the strenght of the vector meson coupling, as well as the Polyakov-loop (PL) potential and the form factors of the covariant model. The latter are constrained by lattice QCD data for the quark propagator. The strength of the vector coupling is adjusted such as to reproduce the slope of the pseudocritical temperature for the chiral phase transition at low chemical potential extracted recently from lattice QCD simulations. Our study supports the existence of a critical endpoint in the QCD phase diagram albeit the constraint for the vector coupling shifts its location to lower temperatures and higher baryochemical potentials than in the case without it.Comment: 23 pages, 10 figures. Version accepted in Phys. Part. Nucl. Lett. (to appear), references adde

Quark exchange model for charmonium dissociation in hot hadronic matter

A diagrammatic approach to quark exchange processes in meson-meson scattering is applied to the case of inelastic reactions of the type (Q\barQ)+(q\barq)\rightarrow (Q\barq) + (q\barQ), where $Q$ and $q$ refer to heavy and light quarks, respectively. This string-flip process is discussed as a microscopic mechanism for charmonium dissociation (absorption) in hadronic matter. The cross section for the reaction $J/\psi + \pi \to D+ \bar D$ is calculated using a potential model, which is fitted to the meson mass spectrum. The temperature dependence of the relaxation time for the \J/Psi distribution in a homogeneous thermal pion gas is obtained. The use of charmonium for the diagnostics of the state of hot hadronic matter produced in ultrarelativistic nucleus-nucleus collisions is discussed.Comment: 24 pages, 3 tables, 7 figure

Core collapse supernovae in the QCD phase diagram

We compare two classes of hybrid equations of state with a hadron-to-quark matter phase transition in their application to core collapse supernova simulations. The first one uses the quark bag model and describes the transition to three-flavor quark matter at low critical densities. The second one employs a Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model with parameters describing a phase transition to two-flavor quark matter at higher critical densities. These models possess a distinctly different temperature dependence of their transition densities which turns out to be crucial for the possible appearance of quark matter in supernova cores. During the early post bounce accretion phase quark matter is found only if the phase transition takes place at sufficiently low densities as in the study based on the bag model. The increase critical density with increasing temperature, as obtained for our PNJL parametrization, prevents the formation of quark matter. The further evolution of the core collapse supernova as obtained applying the quark bag model leads to a structural reconfiguration of the central proto-neutron star where, in addition to a massive pure quark matter core, a strong hydrodynamic shock wave forms and a second neutrino burst is released during the shock propagation across the neutrinospheres. We discuss the severe constraints in the freedom of choice of quark matter models and their parametrization due to the recently observed 2 solar mass pulsar and their implications for further studies of core collapse supernovae in the QCD phase diagram.Comment: 19 pages, 4 figures, CPOD2010 conference proceedin

Neutron star cooling constraints for color superconductivity in hybrid stars

We apply the recently developed Log N - Log S test of compact star cooling theories for the first time to hybrid stars with a color superconducting quark matter core. While there is not yet a microscopically founded superconducting quark matter phase which would fulfill constraints from cooling phenomenology, we explore the hypothetical 2SC+X phase and show that the magnitude and density-dependence of the X-gap can be chosen to satisfy a set of tests: temperature - age (T - t), the brightness constraint, Log N - Log S, and the mass spectrum constraint. The latter test appears as a new conjecture from the present investigation.Comment: 10 pages, 9 figures, 1 tabl

Integral geometry of complex space forms

We show how Alesker's theory of valuations on manifolds gives rise to an algebraic picture of the integral geometry of any Riemannian isotropic space. We then apply this method to give a thorough account of the integral geometry of the complex space forms, i.e. complex projective space, complex hyperbolic space and complex euclidean space. In particular, we compute the family of kinematic formulas for invariant valuations and invariant curvature measures in these spaces. In addition to new and more efficient framings of the tube formulas of Gray and the kinematic formulas of Shifrin, this approach yields a new formula expressing the volumes of the tubes about a totally real submanifold in terms of its intrinsic Riemannian structure. We also show by direct calculation that the Lipschitz-Killing valuations stabilize the subspace of invariant angular curvature measures, suggesting the possibility that a similar phenomenon holds for all Riemannian manifolds. We conclude with a number of open questions and conjectures.Comment: 68 pages; minor change

Neutrino Propagation In Color Superconducting Quark Matter

We calculate the neutrino mean free path in color superconducting quark matter, and employ it to study the cooling of matter via neutrino diffusion in the superconducting phase as compared to a free quark phase. The cooling process slows when quark matter undergoes a second order phase transition to a superconducting phase at the critical temperature $T_c$. Cooling subsequently accelerates as the temperature decreases below $T_c$. This will directly impact the early evolution of a newly born neutron star should its core contain quark matter. Consequently, there may be observable changes in the early neutrino emission which would provide evidence for superconductivity in hot and dense matter.Comment: 12 pages, 5 figure

On the Ground State of Two Flavor Color Superconductor

The diquark condensate susceptibility in neutral color superconductor at moderate baryon density is calculated in the frame of two flavor Nambu-Jona-Lasinio model. When color chemical potential is introduced to keep charge neutrality, the diquark condensate susceptibility is negative in the directions without diquark condensate in color space, which may be regarded as a signal of the instability of the conventional ground state with only diquark condensate in the color 3 direction.Comment: 4 pages, 2 figure

Late time cosmic acceleration from vacuum Brans-Dicke theory in 5D

We show that the scalar-vacuum Brans-Dicke equations in 5D are equivalent to Brans-Dicke theory in 4D with a self interacting potential and an effective matter field. The cosmological implication, in the context of FRW models, is that the observed accelerated expansion of the universe comes naturally from the condition that the scalar field is not a ghost, i.e., $\omega > - 3/2$. We find an effective matter-dominated 4D universe which shows accelerated expansion if $- 3/2 < \omega < - 1$. We study the question of whether accelerated expansion can be made compatible with large values of $\omega$, within the framework of a 5D scalar-vacuum Brans-Dicke theory with variable, instead of constant, parameter $\omega$. In this framework, and based on a general class of solutions of the field equations, we demonstrate that accelerated expansion is incompatible with large values of $\omega$.Comment: In V2 the summary section is expanded. To be published in Classical and Quantum Gravity

The boundary integral method for magnetic billiards

We introduce a boundary integral method for two-dimensional quantum billiards subjected to a constant magnetic field. It allows to calculate spectra and wave functions, in particular at strong fields and semiclassical values of the magnetic length. The method is presented for interior and exterior problems with general boundary conditions. We explain why the magnetic analogues of the field-free single and double layer equations exhibit an infinity of spurious solutions and how these can be eliminated at the expense of dealing with (hyper-)singular operators. The high efficiency of the method is demonstrated by numerical calculations in the extreme semiclassical regime.Comment: 28 pages, 12 figure