2,188 research outputs found
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 , the probability to find the
bare particle in the physical particle, usually satisfies the unitarity bound
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
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
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 supersymmetric nonlinear sigma models. When the
coordinates of the target manifolds have nontrivial anomalous dimensions,
vanishing of the function suggest the existence of novel conformal
field theories whose target space is not Ricci flat. We construct such
conformal field theories with 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
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
Gauge Theoretical Construction of Non-compact Calabi-Yau Manifolds
We construct the non-compact Calabi-Yau manifolds interpreted as the complex
line bundles over the Hermitian symmetric spaces. These manifolds are the
various generalizations of the complex line bundle over CP^{N-1}. Imposing an
F-term constraint on the line bundle over CP^{N-1}, we obtain the line bundle
over the complex quadric surface Q^{N-2}. On the other hand, when we promote
the U(1) gauge symmetry in CP^{N-1} to the non-abelian gauge group U(M), the
line bundle over the Grassmann manifold is obtained. We construct the
non-compact Calabi-Yau manifolds with isometries of exceptional groups, which
we have not discussed in the previous papers. Each of these manifolds contains
the resolution parameter which controls the size of the base manifold, and the
conical singularity appears when the parameter vanishes.Comment: LaTeX2e, 27 pages, no figures, typos correcte
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