Mass Terms in Effective Theories of High Density Quark Matter

We study the structure of mass terms in the effective theory for quasi-particles in QCD at high baryon density. To next-to-leading order in the $1/p_F$ expansion we find two types of mass terms, chirality conserving two-fermion operators and chirality violating four-fermion operators. In the effective chiral theory for Goldstone modes in the color-flavor-locked (CFL) phase the former terms correspond to effective chemical potentials, while the latter lead to Lorentz invariant mass terms. We compute the masses of Goldstone bosons in the CFL phase, confirming earlier results by Son and Stephanov as well as Bedaque and Sch\"afer. We show that to leading order in the coupling constant $g$ there is no anti-particle gap contribution to the mass of Goldstone modes, and that our results are independent of the choice of gauge.Comment: 22 pages, 4 figure

Superdense Matter

We review recent work on the phase structure of QCD at very high baryon density. We introduce the phenomenon of color superconductivity and discuss the use of weak coupling methods. We study the phase structure as a function of the number of flavors and their masses. We also introduce effective theories that describe low energy excitations at high baryon density. Finally, we study the possibility of kaon condensation at very large baryon density.Comment: 13 pages, talk at ICPAQGP, Jaipur, India, Nov. 26-30, 2001; to appear in the proceeding

Hydrodynamic fluctuations and the minimum shear viscosity of the dilute Fermi gas at unitarity

We study hydrodynamic fluctuations in a non-relativistic fluid. We show that in three dimensions fluctuations lead to a minimum in the shear viscosity to entropy density ratio $\eta/s$ as a function of the temperature. The minimum provides a bound on $\eta/s$ which is independent of the conjectured bound in string theory, $\eta/s \geq \hbar/(4\pi k_B)$, where $s$ is the entropy density. For the dilute Fermi gas at unitarity we find \eta/s\gsim 0.2\hbar. This bound is not universal -- it depends on thermodynamic properties of the unitary Fermi gas, and on empirical information about the range of validity of hydrodynamics. We also find that the viscous relaxation time of a hydrodynamic mode with frequency $\omega$ diverges as $1/\sqrt{\omega}$, and that the shear viscosity in two dimensions diverges as $\log(1/ \omega)$.Comment: 26 pages, 5 figures; final version to appear in Phys Rev

Binary Black Hole Coalescence in Semi-Analytic Puncture Evolution

Binary black-hole coalescence is treated semi-analytically by a novel approach. Our prescription employs the conservative Skeleton Hamiltonian that describes orbiting Brill-Lindquist wormholes (termed punctures in Numerical Relativity) within a waveless truncation to the Einstein field equations [G. Faye, P. Jaranowski and G. Sch\"afer, Phys. Rev. D {\bf 69}, 124029 (2004)]. We incorporate, in a transparent Hamiltonian way and in Burke-Thorne gauge structure, the effects of gravitational radiation reaction into the above Skeleton dynamics with the help of 3.5PN accurate angular momentum flux for compact binaries in quasi-circular orbits to obtain a Semi-Analytic Puncture Evolution to model merging black-hole binaries. With the help of the TaylorT4 approximant at 3.5PN order, we perform a {\it first-order} comparison between gravitational wave phase evolutions in Numerical Relativity and our approach for equal-mass binary black holes. This comparison reveals that a modified Skeletonian reactive dynamics that employs flexible parameters will be required to prevent the dephasing between our scheme and Numerical Relativity, similar to what is pursued in the Effective One Body approach. A rough estimate for the gravitational waveform associated with the binary black-hole coalescence in our approach is also provided.Comment: 16 pages, 5 figure

Phases of QCD at High Baryon Density

We review recent work on the phase structure of QCD at very high baryon density. We introduce the phenomenon of color superconductivity and discuss how the quark masses and chemical potentials determine the structure of the superfluid quark phase. We comment on the possibility of kaon condensation at very high baryon density and study the competition between superfluid, density wave, and chiral crystal phases at intermediate density.Comment: 15 pages. To appear in the proceedings of the ECT Workshop on Neutron Star Interiors, Trento, Italy, June 200