141 research outputs found
Construction of N = 2 Chiral Supergravity Compatible with the Reality Condition
We construct N = 2 chiral supergravity (SUGRA) which leads to Ashtekar's
canonical formulation. The supersymmetry (SUSY) transformation parameters are
not constrained at all and auxiliary fields are not required in contrast with
the method of the two-form gravity. We also show that our formulation is
compatible with the reality condition, and that its real section is reduced to
the usual N = 2 SUGRA up to an imaginary boundary term.Comment: 16 pages, late
Supersymmetry algebra in N = 1 chiral supergravity
We consider the supersymmetry (SUSY) transformations in the chiral Lagrangian
for supergravity (SUGRA) with the complex tetrad following the method
used in the usual SUGRA, and present the explicit form of the SUSY
trasformations in the first-order form. The SUSY transformations are generated
by two independent Majorana spinor parameters, which are apparently different
from the constrained parameters employed in the method of the 2-form gravity.
We also calculate the commutator algebra of the SUSY transformations on-shell.Comment: 10 pages, late
Minimal Off-Shell Version of N = 1 Chiral Supergravity
We construct the minimal off-shell formulation of N = 1 chiral supergravity
(SUGRA) introducing a complex antisymmetric tensor field and a
complex axial-vector field as auxiliary fields. The resulting algebra
of the right- and left-handed supersymmetry (SUSY) transformations closes off
shell and generates chiral gauge transforamtions and vector gauge
transformations in addition to the transformations which appear in the case
without auxiliary fields.Comment: 9 pages, late
Canonical formulation of N = 2 supergravity in terms of the Ashtekar variable
We reconstruct the Ashtekar's canonical formulation of N = 2 supergravity
(SUGRA) starting from the N = 2 chiral Lagrangian derived by closely following
the method employed in the usual SUGRA. In order to get the full graded algebra
of the Gauss, U(1) gauge and right-handed supersymmetry (SUSY) constraints, we
extend the internal, global O(2) invariance to local one by introducing a
cosmological constant to the chiral Lagrangian. The resultant Lagrangian does
not contain any auxiliary fields in contrast with the 2-form SUGRA and the SUSY
transformation parameters are not constrained at all. We derive the canonical
formulation of the N = 2 theory in such a manner as the relation with the usual
SUGRA be explicit at least in classical level, and show that the algebra of the
Gauss, U(1) gauge and right-handed SUSY constraints form the graded algebra,
G^2SU(2)(Osp(2,2)). Furthermore, we introduce the graded variables associated
with the G^2SU(2)(Osp(2,2)) algebra and we rewrite the canonical constraints in
a simple form in terms of these variables. We quantize the theory in the
graded-connection representation and discuss the solutions of quantum
constraints.Comment: 19 pages, Latex, corrected some typos and added a referenc
Universally Coupled Massive Gravity, II: Densitized Tetrad and Cotetrad Theories
Einstein's equations in a tetrad formulation are derived from a linear theory
in flat spacetime with an asymmetric potential using free field gauge
invariance, local Lorentz invariance and universal coupling. The gravitational
potential can be either covariant or contravariant and of almost any density
weight. These results are adapted to produce universally coupled massive
variants of Einstein's equations, yielding two one-parameter families of
distinct theories with spin 2 and spin 0. The theories derived, upon fixing the
local Lorentz gauge freedom, are seen to be a subset of those found by
Ogievetsky and Polubarinov some time ago using a spin limitation principle. In
view of the stability question for massive gravities, the proven non-necessity
of positive energy for stability in applied mathematics in some contexts is
recalled. Massive tetrad gravities permit the mass of the spin 0 to be heavier
than that of the spin 2, as well as lighter than or equal to it, and so provide
phenomenological flexibility that might be of astrophysical or cosmological
use.Comment: 2 figures. Forthcoming in General Relativity and Gravitatio
The Seven-sphere and its Kac-Moody Algebra
We investigate the seven-sphere as a group-like manifold and its extension to
a Kac-Moody-like algebra. Covariance properties and tensorial composition of
spinors under are defined. The relation to Malcev algebras is
established. The consequences for octonionic projective spaces are examined.
Current algebras are formulated and their anomalies are derived, and shown to
be unique (even regarding numerical coefficients) up to redefinitions of the
currents. Nilpotency of the BRST operator is consistent with one particular
expression in the class of (field-dependent) anomalies. A Sugawara construction
is given.Comment: 22 pages. Macropackages used: phyzzx, epsf. Three epsf figure files
appende
Hamiltonian structure and noncommutativity in -brane models with exotic supersymmetry
The Hamiltonian of the simplest super -brane model preserving 3/4 of the
D=4 N=1 supersymmetry in the centrally extended symplectic superspace is
derived and its symmetries are described. The constraints of the model are
covariantly separated into the first- and the second-class sets and the Dirac
brackets (D.B.) are constructed. We show the D.B. noncommutativity of the super
-brane coordinates and find the D.B. realization of the
superalgebra. Established is the coincidence of the D.B. and Poisson bracket
realizations of the superalgebra on the constraint surface and the
absence there of anomaly terms in the commutation relations for the quantized
generators of the superalgebra.Comment: Latex, 27 pages, no figures. Latex packages amsfonts and euscript are
use
Poincare gauge invariance and gravitation in Minkowski spacetime
A formulation of Poincare symmetry as an inner symmetry of field theories
defined on a fixed Minkowski spacetime is given. Local P gauge transformations
and the corresponding covariant derivative with P gauge fields are introduced.
The renormalization properties of scalar, spinor and vector fields in P gauge
field backgrounds are determined. A minimal gauge field dynamics consistent
with the renormalization constraints is given.Comment: 36 pages, latex-fil
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