239 research outputs found
Holomorphy, Minimal Homotopy and the 4D, N = 1 Supersymmetric Bardeen-Gross-Jackiw Anomaly
By use of a special homotopy operator, we present an explicit, closed-form
and simple expression for the left-right Bardeen-Gross-Jackiw anomalies
described as the proper superspace integral of a superfunction.Comment: 16 pp, LaTeX, Replacement includes addition comment on WZNW term and
one new referenc
Nonabelian Gauge Theories on Noncommutative Spaces
In this paper, we describe a method for obtaining the nonabelian
Seiberg-Witten map for any gauge group and to any order in theta. The equations
defining the Seiberg-Witten map are expressed using a coboundary operator, so
that they can be solved by constructing a corresponding homotopy operator. The
ambiguities, of both the gauge and covariant type, which arise in this map are
manifest in our formalism.Comment: 14 pages, latex, Talk presented at 2001: A Spacetime Odyssey -
Michigan Center for Theoretical Physics, some typos correcte
Black Hole Entropy and the Dimensional Continuation of the Gauss-Bonnet Theorem
The Euclidean black hole has topology . It is
shown that -in Einstein's theory- the deficit angle of a cusp at any point in
and the area of the are canonical conjugates. The
black hole entropy emerges as the Euler class of a small disk centered at the
horizon multiplied by the area of the there.These results are
obtained through dimensional continuation of the Gauss-Bonnet theorem. The
extension to the most general action yielding second order field equations for
the metric in any spacetime dimension is given.Comment: 7 pages, RevTe
Gravity, Two Times, Tractors, Weyl Invariance and Six Dimensional Quantum Mechanics
Fefferman and Graham showed some time ago that four dimensional conformal
geometries could be analyzed in terms of six dimensional, ambient, Riemannian
geometries admitting a closed homothety. Recently it was shown how conformal
geometry provides a description of physics manifestly invariant under local
choices of unit systems. Strikingly, Einstein's equations are then equivalent
to the existence of a parallel scale tractor (a six component vector subject to
a certain first order covariant constancy condition at every point in four
dimensional spacetime). These results suggest a six dimensional description of
four dimensional physics, a viewpoint promulgated by the two times physics
program of Bars. The Fefferman--Graham construction relies on a triplet of
operators corresponding, respectively to a curved six dimensional light cone,
the dilation generator and the Laplacian. These form an sp(2) algebra which
Bars employs as a first class algebra of constraints in a six-dimensional gauge
theory. In this article four dimensional gravity is recast in terms of six
dimensional quantum mechanics by melding the two times and tractor approaches.
This "parent" formulation of gravity is built from an infinite set of six
dimensional fields. Successively integrating out these fields yields various
novel descriptions of gravity including a new four dimensional one built from a
scalar doublet, a tractor vector multiplet and a conformal class of metrics.Comment: 27 pages, LaTe
Topological Invariants, Instantons and Chiral Anomaly on Spaces with Torsion
In a spacetime with nonvanishing torsion there can occur topologically stable
configurations associated with the frame bundle which are independent of the
curvature. The relevant topological invariants are integrals of local scalar
densities first discussed by Nieh and Yan (N-Y). In four dimensions, the N-Y
form is the only closed
4-form invariant under local Lorentz rotations associated with the torsion of
the manifold. The integral of over a compact D-dimensional (Euclidean)
manifold is shown to be a topological invariant related to the Pontryagin
classes of SO(D+1) and SO(D). An explicit example of a topologically nontrivial
configuration carrying nonvanishing instanton number proportional to
is costructed. The chiral anomaly in a four-dimensional spacetime with torsion
is also shown to contain a contribution proportional to , besides the usual
Pontryagin density related to the spacetime curvature. The violation of chiral
symmetry can thus depend on the instanton number of the tangent frame bundle of
the manifold. Similar invariants can be constructed in D>4 dimensions and the
existence of the corresponding nontrivial excitations is also discussed.Comment: 6 pages, RevTeX, no figures, two column
Mass, Confinement and CP Invariance in the Seiberg-Witten Model"
Several physics aspects of the Seiberg-Witten solution of N=2 supersymmetric
Yang-Mills theory with SU(2) gauge group, supplemented with a small mass term
for the "matter" fields which leads to an theory with confinement, are
discussed. The light spectrum of the theory is understood on the basis of
current algebra relations, and CP invariance of the massless and massive
theories is studied. We find that in the massive (confining) theory the low
energy physics has an exact CP symmetry, while in a generic vacuum in the
massless theory CP invarince is spontaneously broken.Comment: Latex file, 13 pages, plus 1 eps Figure file (Revised
A Method for Simulating Chiral Fermions on the Lattice
A method for simulating chiral gauge theories on the lattice is proposed,
involving zeromodes on a topological defect. Lattice doublers may be decoupled
in a gauge invariant manner, and flavor anomalies can be directly observed on a
finite lattice. (Requires harvmac)Comment: 10 pages, UCSD-PTH-92-1
Generic chiral superfield model on nonanticommutative N=1/2 superspace
We consider the generic nonanticommutative model of chiral-antichiral
superfields on superspace. The model is formulated in
terms of an arbitrary K\"ahlerian potential, chiral and antichiral
superpotentials and can include the nonanticommutative supersymmetric
sigma-model as a partial case. We study a component structure of the model and
derive the component Lagrangian in an explicit form with all auxiliary fields
contributions. We show that the infinite series in the classical action for
generic nonanticommutative model of chiral-antichiral superfields in D=4
dimensions can be resumed in a compact expression which can be written as a
deformation of standard Zumino's lagrangian and chiral superpotential. Problem
of eliminating the auxiliary fields in the generic model is discussed and the
first perturbative correction to the effective scalar potential is obtained.Comment: 12 pages, LaTeX; text revised and extended, references adde
CPT and Other Symmetries in String/M Theory
We initiate a search for non-perturbative consistency conditions in M theory.
Some non-perturbative conditions are already known in Type I theories; we
review these and search for others. We focus principally on possible anomalies
in discrete symmetries. It is generally believed that discrete symmetries in
string theories are gauge symmetries, so anomalies would provide evidence for
inconsistencies. Using the orbifold cosmic string construction, we give some
evidence that the symmetries we study are gauged. We then search for anomalies
in discrete symmetries in a variety of models, both with and without
supersymmetry. In symmetric orbifold models we extend previous searches, and
show in a variety of examples that all anomalies may be canceled by a
Green-Schwarz mechanism. We explore some asymmetric orbifold constructions and
again find that all anomalies may be canceled this way. Then we turn to Type
IIB orientifold models where it is known that even perturbative anomalies are
non-universal. In the examples we study, by combining geometric discrete
symmetries with continuous gauge symmetries, one may define non-anomalous
discrete symmetries already in perturbation theory; in other cases, the
anomalies are universal. Finally, we turn to the question of CPT conservation
in string/M theory. It is well known that CPT is conserved in all string
perturbation expansions; here in a number of examples for which a
non-perturbative formulation is available we provide evidence that it is
conserved exactly.Comment: 52 pages.1 paragraph added in introduction to clarify assumption
Dualities of the Matrix Model from T-Duality of the Type II String
We investigate in the Matrix theory framework, the subgroup of dualities of
the DLCQ of M-theory compactified on three-tori, which corresponds to T-duality
in the auxiliary Type II string theory. We show how these dualities are
realized in the supersymmetric Yang-Mills gauge theories on dual noncommutative
three-tori.Comment: 37 pages, LaTeX, no figures, typos correcte
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