683 research outputs found

    Conformal Sigma Models with Anomalous Dimensions and Ricci Solitons

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    We present new non-Ricci-flat Kahler metrics with U(N) and O(N) isometries as target manifolds of superconformally invariant sigma models with an anomalous dimension. They are so-called Ricci solitons, special solutions to a Ricci-flow equation. These metrics explicitly contain the anomalous dimension and reduce to Ricci-flat Kahler metrics on the canonical line bundles over certain coset spaces in the limit of vanishing anomalous dimension.Comment: 9 pages, no figure

    Unitarity Bound of the Wave Function Renormalization Constant

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    The wave function renormalization constant ZZ, the probability to find the bare particle in the physical particle, usually satisfies the unitarity bound 0≀Z≀10 \leq Z \leq 1 in field theories without negative metric states. This unitarity bound implies the positivity of the anomalous dimension of the field in the one-loop approximation. In nonlinear sigma models, however, this bound is apparently broken because of the field dependence of the canonical momentum. The contribution of the bubble diagrams to the anomalous dimension can be negative, while the contributions from more than two particle states satisfies the positivity of the anomalous dimension as expected. We derive the genuine unitarity bound of the wave function renormalization constant.Comment: 8 pages, 2 figures, comments adde

    Three Dimensional Nonlinear Sigma Models in the Wilsonian Renormalization Method

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    The three dimensional nonlinear sigma model is unrenormalizable in perturbative method. By using the ÎČ\beta function in the nonperturbative Wilsonian renormalization group method, we argue that N=2{\cal N}=2 supersymmetric nonlinear σ\sigma models are renormalizable in three dimensions. When the target space is an Einstein-K\"{a}hler manifold with positive scalar curvature, such as CPNP^N or QNQ^N, there are nontrivial ultraviolet (UV) fixed point, which can be used to define the nontrivial continuum theory. If the target space has a negative scalar curvature, however, the theory has only the infrared Gaussian fixed point, and the sensible continuum theory cannot be defined. We also construct a model which interpolates between the CPNP^N and QNQ^N models with two coupling constants. This model has two non-trivial UV fixed points which can be used to define the continuum theory. Finally, we construct a class of conformal field theories with SU(N){\bf SU}(N) symmetry, defined at the fixed point of the nonperturbative ÎČ\beta function. These conformal field theories have a free parameter corresponding to the anomalous dimension of the scalar fields. If we choose a specific value of the parameter, we recover the conformal field theory defined at the UV fixed point of CPNP^N model and the symmetry is enhanced to SU(N+1){\bf SU}(N+1).Comment: 16 pages, 1 figure, references adde

    Normal Coordinates in Kahler Manifolds and the Background Field Method

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    Riemann normal coordinates (RNC) are unsuitable for Kahler manifolds since they are not holomorphic. Instead, Kahler normal coordinates (KNC) can be defined as holomorphic coordinates. We prove that KNC transform as a holomorphic tangent vector under holomorphic coordinate transformations, and therefore they are natural extensions of RNC to the case of Kahler manifolds. The KNC expansion provides the manifestly covariant background field method preserving the complex structure in supersymmetric nonlinear sigma models

    Latent heat in the chiral phase transition

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    The chiral phase transition at finite temperature and density is discussed in the framework of the QCD-like gauge field theory. The thermodynamical potential is investigated using a variational approach. Latent heat generated in the first-order phase transition is calculated. It is found that the latent heat is enhanced near the tricritical point and is more than several hundred MeV per quark.Comment: 6 pages, 3 figure

    Solving the Schwinger-Dyson Equations for Gluodynamics in the Maximal Abelian Gauge

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    We derive the Schwinger-Dyson equations for the SU(2) Yang-Mills theory in the maximal Abelian gauge and solve them in the infrared asymptotic region. We find that the infrared asymptotic solutions for the gluon and ghost propagators are consistent with the hypothesis of Abelian dominance.Comment: 3 pages, 1 figure; Lattice2003(topology

    Chiral phase transition at high temperature in the QCD-like gauge theory

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    The chiral phase transition at high temperature is investigated using the effect ive potential in the framework of the QCD-like gauge theory with a variational a pproach. We have a second order phase transition at Tc=136T_c=136MeV. We also investigate numerically the temperature dependence of condensate, fπf_\pi a nd a2(T)a_2(T)(coefficient of the quadratic term in the effective potential) and es timate the critical exponents of these quantities.Comment: 12 pages,7 figure

    Structure of Strange Dwarfs with Color Superconducting Core

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    We study effects of two-flavor color superconductivity on the structure of strange dwarfs, which are stellar objects with similar masses and radii with ordinary white dwarfs but stabilized by the strange quark matter core. We find that unpaired quark matter is a good approximation to the core of strange dwarfs.Comment: 8 pages 5 figures, J. Phys. G, accepte
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