42 research outputs found
Multi-plaquette solutions for discretized Ashtekar gravity
A discretized version of canonical quantum gravity proposed by Loll is
investigated. After slightly modifying Loll's discretized Hamiltonian
constraint, we encode its action on the spin network states in terms of
combinatorial topological manipulations of the lattice loops. Using this
topological formulation we find new solutions to the discretized Wheeler-Dewitt
equation. These solutions have their support on the connected set of
plaquettes. We also show that these solutions are not normalizable with respect
to the induced heat-kernel measure on gauge theories.Comment: 11 pages Latex (2 figures available as a postscript file, the rough
discussion on the non-normalizability has been made exact.
Transition Amplitude in 2+1 dimensional Chern-Simons Gravity on a Torus
The discussions on the modular invariance in section 5 are refined.Comment: 21 pages, Late
Ashtekar's formulation for supergravities as "constrained" BF theories
It is known that Ashtekar's formulation for pure Einstein gravity can be cast
into the form of a topological field theory, namely the BF theory, with
the B-fields subject to an algebraic constraint. We extend this relation
between Ashtekar's formalism and BF theories to and supergravities.
The relevant gauge groups in these cases become graded Lie groups of
which are generated by left-handed local Lorentz transformations and
left-supersymmetry transformations. As a corollary of these relations, we
provide topological solutions for supergravity with a vanishing
cosmological constant. It is also shown that, due to the algebraic constraints,
the Kalb-Ramond symmetry which is characteristic of BF theories breaks down to
the symmetry under diffeomorphisms and right-supersymmetry transformations.Comment: 26 pages Latex (references added
Matrix Model for Dirichlet Open String
We discuss the open string ending on D -branes in IKKT framework. First we
determine the boundary conditions of Green-Schwarz superstring which are
consistent with supersymmetry and -symmetry. We point out some
subtleties arising from taking the Schild gauge and show that in this gauge the
system incorporates the limited dimensional D -branes (). The matrix
regularization for the Dirichlet open string is given by gauge group SO(N).
When , the matrix model becomes the dimensional reduction of a 6
dimensional super Yang-Mills theory.Comment: 9 pages, LaTe
Addendum to "Classical and Quantum Evolutions of the de Sitter and the anti-de Sitter Universes in 2+1 dimensions"
The previous discussion \cite{ezawa} on reducing the phase space of the first
order Einstein gravity in 2+1 dimensions is reconsidered. We construct a \lq\lq
correct" physical phase space in the case of positive cosmological constant,
taking into account the geometrical feature of SO(3,1) connections. A
parametrization which unifies the two sectors of the physical phase space is
also given.Comment: Latex 8 pages (Crucial and essential changes have been made.
BPS Configuration of Supermembrane With Winding in M-direction
We study de Wit-Hoppe-Nicolai supermembrane with emphasis on the winding in
M-direction. We propose a SUSY algebra of the supermembrane in the Lorentz
invariant form. We analyze the BPS conditions and argue that the area
preserving diffeomorphism constraints associated with the harmonic vector
fields play an essential role. We derive the first order partial differential
equation that describes the BPS state with one quarter SUSY.Comment: 10 pages latex, references adde
Combinatorial solutions to the Hamiltonian constraint in (2+1)-dimensional Ashtekar gravity
Dirac's quantization of the (2+1)-dimensional analog of Ashtekar's approach
to quantum gravity is investigated. After providing a diffeomorphism-invariant
regularization of the Hamiltonian constraint, we find a set of solutions to
this Hamiltonian constraint which is a generalization of the solution
discovered by Jacobson and Smolin. These solutions are given by particular
linear combinations of the spin network states. While the classical
counterparts of these solutions have degenerate metric, due to a \lq quantum
effect' the area operator has nonvanishing action on these states. We also
discuss how to extend our results to (3+1)-dimensions.Comment: 41 pages Latex (2 figures available as a postscript file