Differential Regularization of a Non-relativistic Anyon Model

Differential regularization is applied to a field theory of a non-relativistic charged boson field $\phi$ with $\lambda (\phi {}^{*} \phi)^2$ self-interaction and coupling to a statistics-changing $U(1)$ Chern-Simons gauge field. Renormalized configuration-space amplitudes for all diagrams contributing to the $\phi {}^{*} \phi {}^{*} \phi \phi$ 4-point function, which is the only primitively divergent Green's function, are obtained up to 3-loop order. The renormalization group equations are explicitly checked, and the scheme dependence of the $\beta$-function is investigated. If the renormalization scheme is fixed to agree with a previous 1-loop calculation, the 2- and 3-loop contributions to $\beta(\lambda,e)$ vanish, and $\beta(\lambda,e)$ itself vanishes when the ``self-dual'' condition relating $\lambda$ to the gauge coupling $e$ is imposed.Comment: 22 pages in ReVTEX (with a plaintext PostScript figure appended at end), MIT CTP #221

Inclusive charged-current neutrino-nucleus reactions calculated with the relativistic quasiparticle random phase approximation

Inclusive neutrino-nucleus cross sections are calculated using a consistent relativistic mean-field theoretical framework. The weak lepton-hadron interaction is expressed in the standard current-current form, the nuclear ground state is described with the relativistic Hartree-Bogoliubov model, and the relevant transitions to excited nuclear states are calculated in the relativistic quasiparticle random phase approximation. Illustrative test calculations are performed for charged-current neutrino reactions on $^{12}$C, $^{16}$O, $^{56}$Fe, and $^{208}$Pb, and results compared with previous studies and available data. Using the experimental neutrino fluxes, the averaged cross sections are evaluated for nuclei of interest for neutrino detectors. We analyze the total neutrino-nucleus cross sections, and the evolution of the contribution of the different multipole excitations as a function of neutrino energy. The cross sections for reactions of supernova neutrinos on $^{16}$O and $^{208}$Pb target nuclei are analyzed as functions of the temperature and chemical potential.Comment: 28 pages, 8 figures, 2 tables, submitted to Phys. Rev.

Continuous distributions of D3-branes and gauged supergravity

States on the Coulomb branch of N=4 super-Yang-Mills theory are studied from the point of view of gauged supergravity in five dimensions. These supersymmetric solutions provide examples of consistent truncation from type IIB supergravity in ten dimensions. A mass gap for states created by local operators and perfect screening for external quarks arise in the supergravity approximation. We offer an interpretation of these surprising features in terms of ensembles of brane distributions.Comment: 19 pages, two figures, latex. v2: reference added, small corrections. v3: corrected unbounded spectrum erro

Renormalization Group Flows from Holography--Supersymmetry and a c-Theorem

We obtain first order equations that determine a supersymmetric kink solution in five-dimensional N=8 gauged supergravity. The kink interpolates between an exterior anti-de Sitter region with maximal supersymmetry and an interior anti-de Sitter region with one quarter of the maximal supersymmetry. One eighth of supersymmetry is preserved by the kink as a whole. We interpret it as describing the renormalization group flow in N=4 super-Yang-Mills theory broken to an N=1 theory by the addition of a mass term for one of the three adjoint chiral superfields. A detailed correspondence is obtained between fields of bulk supergravity in the interior anti-de Sitter region and composite operators of the infrared field theory. We also point out that the truncation used to find the reduced symmetry critical point can be extended to obtain a new N=4 gauged supergravity theory holographically dual to a sector of N=2 gauge theories based on quiver diagrams. We consider more general kink geometries and construct a c-function that is positive and monotonic if a weak energy condition holds in the bulk gravity theory. For even-dimensional boundaries, the c-function coincides with the trace anomaly coefficients of the holographically related field theory in limits where conformal invariance is recovered.Comment: 56 pages, three figures, harvmac. v2: improved referencing, corrected discussion of energy conditions. v3: one more reference fixe

Brane Worlds in Collision

We obtain an exact solution of the supergravity equations of motion in which the four-dimensional observed universe is one of a number of colliding D3-branes in a Calabi-Yau background. The collision results in the ten-dimensional spacetime splitting into disconnected regions, bounded by curvature singularities. However, near the D3-branes the metric remains static during and after the collision. We also obtain a general class of solutions representing $p$-brane collisions in arbitrary dimensions, including one in which the universe ends with the mutual annihilation of a positive-tension and negative-tension 3-brane.Comment: RevTex, 4 pages, 1 figure, typos and minor errors correcte

Neutrino mass constraint from CMB and its degeneracy with other cosmological parameters

We show that the cosmic microwave background (CMB) data of WMAP can give subelectronvolt limit on the neutrino mass: m_nu < 0.63 eV (95% CL). We also investigate its degeneracy with other cosmological parameters. In particular, we show the Hubble constant derived from the WMAP data decreases considerably when the neutrino mass is a few times 0.1 eV.Comment: 3 pages, 2 figures, prepared for the TAUP2007 Proceeding

pp Wave Big Bangs: Matrix Strings and Shrinking Fuzzy Spheres

We find pp wave solutions in string theory with null-like linear dilatons. These provide toy models of big bang cosmologies. We formulate Matrix String Theory in these backgrounds. Near the big bang ``singularity'', the string theory becomes strongly coupled but the Yang-Mills description of the matrix string is weakly coupled. The presence of a second length scale allows us to focus on a specific class of non-abelian configurations, viz. fuzzy cylinders, for a suitable regime of parameters. We show that, for a class of pp waves, fuzzy cylinders which start out big at early times dynamically shrink into usual strings at sufficiently late times.Comment: 29 pages, ReVTeX and AMSLaTeX. 4 Figures. v2: Typo corrected and reference adde

Phase transition and hybrid star in a SU(2) chiral sigma model

We use a modified SU(2) chiral sigma model to study nuclear matter at high density using mean field approach. We also study the phase transition of nuclear matter to quark matter in the interior of highly dense neutron stars. Stable solutions of Tolman-Oppenheimer-Volkoff equations representing hybrid stars are obtained with a maximum mass of 1.69 $M_{\odot}$, radii around 9.3 kms and a quark matter core constituting nearly 55-85 % of the star radii.Comment: 19 pages, 9 figures, accepted for Mod. Phys. Letts.

A perturbative re-analysis of N=4 supersymmetric Yang--Mills theory

The finiteness properties of the N=4 supersymmetric Yang-Mills theory are reanalyzed both in the component formulation and using N=1 superfields, in order to discuss some subtleties that emerge in the computation of gauge dependent quantities. The one-loop corrections to various Green functions of elementary fields are calculated. In the component formulation it is shown that the choice of the Wess-Zumino gauge, that is standard in supersymmetric gauge theories, introduces ultraviolet divergences in the propagators at the one-loop level. Such divergences are exactly cancelled when the contributions of the fields that are put to zero in the Wess-Zumino gauge are taken into account. In the description in terms of N=1 superfields infrared divergences are found for every choice of gauge different from the supersymmetric generalization of the Fermi-Feynman gauge. Two-, three- and four-point functions of N=1 superfields are computed and some general features of the infrared problem are discussed. We also examine the effect of the introduction of mass terms for the (anti) chiral superfields in the theory, which break supersymmetry from N=4 to N=1. It is shown that in the mass deformed model no ultraviolet divergences appear in two-point functions. It argued that this result can be generalized to n-point functions, supporting the proposal of a possible of use of this modified model as a supersymmetry-preserving regularization scheme for N=1 theories.Comment: 41 pages, LaTeX2e, uses feynMP package to draw Feynman diagram

Color superconductivity in weak coupling

We derive perturbatively the gap equations for a color-superconducting condensate with total spin J=0 in dense QCD. At zero temperature, we confirm the results of Son for the dependence of the condensate on the coupling constant, and compute the prefactor to leading logarithmic accuracy. At nonzero temperature, we find that to leading order in weak coupling, the temperature dependence of the condensate is identical to that in BCS-like theories. The condensates for total spin J=1 are classified; to leading logarithmic accuracy these condensates are of the same order as those of spin J=0.Comment: 30 pages, 3 figures, RevTeX, epsf and psfig style files require