On the QCD Phase Transition at Finite Baryon Density

We investigate the QCD chiral phase transition at finite chemical potential $\mu$, using the renormalization group (RG) to characterize the infrared behavior of sigma models constrained by the flavor and spacetime symmetries. The results are similar to those obtained from RG analysis of the finite temperature transition at zero baryon density. When there are more than two massless flavors of quarks, a first order transition is predicted for the entire phase boundary. In the two flavor case, a boundary with first and second order regions separated by a tricritical point seems most likely. We discuss the real-world case with two light quarks and an intermediate mass strange quark. Improved lattice data on the temperature transition will strongly constrain the possibilities for the phase boundary.Comment: 10 pages, 2 figures, Latex. Added discussion on realistic strange quark mass and recent lattice dat

Neutron Star Vortex Dynamics and Magnetic Field Decay: Implications for High Density Nuclear Matter

We investigate the effect of the density-dependent proton and neutron gaps on vortex dynamics in neutron stars. We argue that the persistence of neutron star magnetic fields on timescales of $10^9$ y suggests a superconducting gap curve with local maximum at intermediate density. We discuss the implications for exotic core phenomena such as pion/kaon condensation or a transition to quark matter.Comment: 7 pages, 2 figures, uses LaTe

On the volatility of volatility

The Chicago Board Options Exchange (CBOE) Volatility Index, VIX, is calculated based on prices of out-of-the-money put and call options on the S&P 500 index (SPX). Sometimes called the "investor fear gauge," the VIX is a measure of the implied volatility of the SPX, and is observed to be correlated with the 30-day realized volatility of the SPX. Changes in the VIX are observed to be negatively correlated with changes in the SPX. However, no significant correlation between changes in the VIX and changes in the 30-day realized volatility of the SPX are observed. We investigate whether this indicates a mispricing of options following large VIX moves, and examine the relation to excess returns from variance swaps.Comment: 15 pages, 12 figures, LaTe

Cosmology of Nonlinear Oscillations

The nonlinear oscillations of a scalar field are shown to have cosmological equations of state with $w = p / \rho$ ranging from $-1 < w < 1$. We investigate the possibility that the dark energy is due to such oscillations.Comment: 5 pages, latex. References added; to appear in PL

Gradient instability for ω < - 1

We show that in single scalar field models of the dark energy with equations of state satisfying w ≡ p/ρ < − 1, the effective Lagrangian for fluctuations about the homogeneous background has a wrong sign spatial kinetic term. In most cases, spatial gradients are ruled out by microwave background observations. The sign of w + 1 is not connected to the sign of the time derivative kinetic term in the effective Lagrangian

Instabilities and the null energy condition

We show that violation of the null energy condition implies instability in a broad class of models, including classical gauge theories with scalar and fermionic matter as well as any perfect fluid. When applied to the dark energy, our results imply that $w = p / \rho$ is unlikely to be less than -1.Comment: 5 pages, 1 figure, revtex, presentation improved, minor change

Magnetic Interactions, the Renormalization Group and Color Superconductivity in High Density QCD

We investigate the effect of long range magnetic interactions on the renormalization group (RG) evolution of local Cooper pairing interactions near the Fermi surface in high density QCD. We use an explicit cut-off on momentum modes, with special emphasis on screening effects such as Landau damping, to derive the RG equations in a gauge invariant, weak coupling expansion. We obtain the Landau pole $\Delta \sim \mu g^{-5} \exp(- \frac{3 \pi^2}{\sqrt{2} g})$, although the structure of our equations differs from previous results. We also investigate the gap equation, including condensates of higher angular momentum. We show that rotational invariance is unbroken at asymptotically high density, and verify that $\Delta$ is the correct value of the gap when higher modes are included in the analysis.Comment: 17 pages, 3 figures, late

Anomaly Induced QCD Potential and Quark Decoupling

We explore the anomaly induced effective QCD meson potential in the framework of the effective Lagrangian approach. We suggest a decoupling procedure, when a flavored quark becomes massive, which mimics the one employed by Seiberg for supersymmetric gauge theories. It is seen that, after decoupling, the QCD potential naturally converts to the one with one less flavor. We study the N_c and N_f dependence of the \eta^{\prime} mass

Black hole entropy, curved space and monsters

We investigate the microscopic origin of black hole entropy, in particular the gap between the maximum entropy of ordinary matter and that of black holes. Using curved space, we construct configurations with entropy greater than their area in Planck units. These configurations have pathological properties and we refer to them as monsters. When monsters are excluded we recover the entropy bound on ordinary matter $S < A^{3/4}$. This bound implies that essentially all of the microstates of a semiclassical black hole are associated with the growth of a slightly smaller black hole which absorbs some additional energy. Our results suggest that the area entropy of black holes is the logarithm of the number of distinct ways in which one can form the black hole from ordinary matter and smaller black holes, but only after the exclusion of monster states.Comment: 5 pages, revtex. Final version to appear Physics Letters

A Note on Supersymmetry Breaking

Using a simple observation based on holomorphy, we argue that any model which spontaneously breaks supersymmetry for some range of a parameter will do so generically for all values of that parameter, modulo some isolated exceptional points. Conversely, a model which preserves supersymmetry for some range of a parameter will also do so everywhere except at isolated exceptional points. We discuss how these observations can be useful in the construction of new models which break supersymmetry and discuss some simple examples. We also comment on the relation of these results to the Witten index.Comment: 10 pages, LaTeX. Additional reference added, minor change to last subsectio