Auxiliary Field Methods in Supersymmetric Nonlinear Sigma Models

Auxiliary field methods in D=2 (or 3), N=2 supersymmetric (SUSY) nonlinear sigma models (NLSMs) are studied. For these models auxiliary fields as Lagrange multipliers belong to a vector or a chiral superfield, which gives a Kahler quotient of complexified gauge group or a holomorphic constraint on it, respectively. Using these, NLSMs on all Hermitian symmetric spaces were formulated previously. In this paper, we formulate new SUSY NLSMs on some rank-two Kahler coset spaces as SUSY gauge theories with two Fayet-Iliopoulos parameters.Comment: 42 pages, no figure

Conformal Sigma Models with Anomalous Dimensions and Ricci Solitons

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

Structure change of Cooper pairs in color superconductivity -- Crossover from BCS to BEC ? --

We discuss a possibility of transition from color superconductivity of the standard BCS type at high density, to Bose-Einstein Condensation (BEC) of Cooper pairs at lower density. Examining two-flavor QCD over a wide range of baryon density, we found the size of a Cooper pair becomes small enough to be comparable to the averaged quark-quark distance at lower density. We also consider the same problem in two-color QCD.Comment: 4pages, 2figures, Contribution to the Proceedings of "Quark Matter 2002", Nantes, France, 18-24 Jul 200

Unitarity Bound of the Wave Function Renormalization Constant

The wave function renormalization constant $Z$, the probability to find the bare particle in the physical particle, usually satisfies the unitarity bound $0 \leq Z \leq 1$ 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

A New Class of Conformal Field Theories with Anomalous Dimensions

The Wilsonian renormalization group (WRG) equation is used to derive a new class of scale invariant field theories with nonvanishing anomalous dimensions in 2-dimensional ${\cal N}=2$ supersymmetric nonlinear sigma models. When the coordinates of the target manifolds have nontrivial anomalous dimensions, vanishing of the $\beta$ function suggest the existence of novel conformal field theories whose target space is not Ricci flat. We construct such conformal field theories with ${\bf U}(N)$ symmetry. The theory has one free parameter a corresponding to the anomalous dimension of the scalar fields. The new conformal field theories are well behaved for positive a and have the central charge 3N, while they have curvature singularities at the boundary for a<0. When the target space is of complex 1-dimension, we obtain the explicit form of the Lagrangian, which reduces to two different kinds of free field theories in weak and in strong coupling limit. As a consistency test, the anomalous dimensions are reproduced in these two limits. The target space in this case looks like a semi-infinite cigar with one-dimension compactified to a circle.Comment: 14 pages, 3 figures; comments and references adde

Quantum Equivalence of Auxiliary Field Methods in Supersymmetric Theories

Quantum corrections to Legendre transformations are shown to cancel to all orders in supersymmetric theories in path integral formalism. Using this result, lagrangians for auxiliary fields are generalized to non-quadratic forms. In supersymmetric effective nonlinear lagrangians, the arbitrariness due to the existence of quasi Nambu-Goldstone bosons is shown to disappear when local auxiliary gauge fields are introduced.Comment: 17 pages, LaTeX, no figures, the version to appear in Prog. Theor. Phys. 103 (2000

Construction of Supergravity Backgrounds with a Dilaton Field

A new class of non-compact Kahler backgrounds accompanied by a non-constant dilaton field is constructed as a supergravity solution. It is interpreted as a complex line bundle over a base manifold comprising of a combination of arbitrary coset spaces, and also includes the case of Calabi-Yau manifolds. The resulting backgrounds have U(1) isometry. We consider N=2 supersymmetric sigma-models on them, and derive a non-Kahlerian solution by U(1) duality transformation, which preserves N=2 supersymmetry.Comment: 13 pages, minor correction