Phase Transitions of Charged Scalars at Finite Temperature and Chemical Potential

We calculate the grand canonical partition function at the one-loop level for scalar quantum electrodynamics at finite temperature and chemical potential. A classical background charge density with a charge opposite that of the scalars ensures the neutrality of the system. For low density systems we find evidence of a first order phase transition. We find upper and lower bounds on the transition temperature below which the charged scalars form a condensate. A first order phase transition may have consequences for helium-core white dwarf stars in which it has been argued that such a condensate of charged helium-4 nuclei could exist.Comment: 20 pages, 3 figures. Version accepted for publication in JHE

Field Theory for a Deuteron Quantum Liquid

Based on general symmetry principles we study an effective Lagrangian for a neutral system of condensed spin-1 deuteron nuclei and electrons, at greater-than-atomic but less-than-nuclear densities. We expect such matter to be present in thin layers within certain low-mass brown dwarfs. It may also be produced in future shock-wave-compression experiments as an effective fuel for laser induced nuclear fusion. We find a background solution of the effective theory describing a net spin zero condensate of deuterons with their spins aligned and anti-aligned in a certain spontaneously emerged preferred direction. The spectrum of low energy collective excitations contains two spin waves with linear dispersions -- like in antiferromagnets -- as well as gapped longitudinal and transverse modes related to the Meissner effect -- like in superconductors. We show that counting of the Nambu-Goldstone modes of spontaneously broken internal and space-time symmetries obeys, in a nontrivial way, the rules of the Goldstone theorem for Lorentz non-invariant systems. We discuss thermodynamic properties of the condensate, and its potential manifestation in the low-mass brown dwarfs.Comment: 19 LaTeX pages; v2: 2 refs added, JHEP versio

Softly Massive Gravity

Large-distance modification of gravity may be the mechanism for solving the cosmological constant problem. A simple model of the large-distance modification -- four-dimensional (4D) gravity with the hard mass term-- is problematic from the theoretical standpoint. Here we discuss a different model, the brane-induced gravity, that effectively introduces a soft graviton mass. We study the issues of unitarity, analyticity and causality in this model in more than five dimensions. We show that a consistent prescription for the poles of the Green's function can be specified so that 4D unitarity is preserved. However, in certain instances 4D analyticity cannot be maintained when theory becomes higher dimensional. As a result, one has to sacrifice 4D causality at distances of the order of the present-day Hubble scale. This is a welcome feature for solving the cosmological constant problem, as was recently argued in the literature. We also show that, unlike the 4D massive gravity, the model has no strong-coupling problem at intermediate scales.Comment: 33 LaTex page

Metastable Gravitons and Infinite Volume Extra Dimensions

We address the issue of whether extra dimensions could have an infinite volume and yet reproduce the effects of observable four-dimensional gravity on a brane. There is no normalizable zero-mode graviton in this case, nevertheless correct Newton's law can be obtained by exchanging bulk gravitons. This can be interpreted as an exchange of a single {\it metastable} 4D graviton. Such theories have remarkable phenomenological signatures since the evolution of the Universe becomes high-dimensional at very large scales. Furthermore, the bulk supersymmetry in the infinite volume limit might be preserved while being completely broken on a brane. This gives rise to a possibility of controlling the value of the bulk cosmological constant. Unfortunately, these theories have difficulties in reproducing certain predictions of Einstein's theory related to relativistic sources. This is due to the van Dam-Veltman-Zakharov discontinuity in the propagator of a massive graviton. This suggests that all theories in which contributions to effective 4D gravity come predominantly from the bulk graviton exchange should encounter serious phenomenological difficulties.Comment: 9 LaTex pages; One reference and a comment adde