205 research outputs found
A Quasiperiodic Gibbons--Hawking Metric and Spacetime Foam
We present a quasiperiodic self-dual metric of the Gibbons--Hawking type with
one gravitational instanton per spacetime cell. The solution, based on an
adaptation of Weierstrassian and functions to three
dimensions, conforms to a definition of spacetime foam given by Hawking.Comment: 14 pages, Late
Solutions in Self-Dual Gravity Constructed Via Chiral Equations
The chiral model for self-dual gravity given by Husain in the context of the
chiral equations approach is discussed. A Lie algebra corresponding to a finite
dimensional subgroup of the group of symplectic diffeomorphisms is found, and
then use for expanding the Lie algebra valued connections associated with the
chiral model. The self-dual metric can be explicitly given in terms of harmonic
maps and in terms of a basis of this subalgebra.Comment: Plain Latex, 13 Pages, major revisions of style in the above proof,
several Comments added. Version to appear in Physical Review
The gravity dual of supersymmetric gauge theories on a two-parameter deformed three-sphere
We present rigid supersymmetric backgrounds for three-dimensional N=2
supersymmetric gauge theories, comprising a two-parameter U(1)xU(1)-invariant
deformed three-sphere, and their gravity duals. These are described by
supersymmetric solutions of four-dimensional N=2 gauged supergravity with a
self-dual metric on the ball and different instantons for the graviphoton
field. We find two types of solutions, distinguished by their holographic free
energies. In one type the holographic free energy is constant, whereas in
another type it depends in a simple way on the parameters and is generically
complex. This leads to a conjecture for the localized partition function of a
class of N=2 supersymmetric gauge theories on these backgrounds.Comment: 27 pages, 1 figure; v2: typos fixed, minor changes, one reference
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Non-Abelian pp-waves in D=4 supergravity theories
The non-Abelian plane waves, first found in flat spacetime by Coleman and
subsequently generalized to give pp-waves in Einstein-Yang-Mills theory, are
shown to be 1/2 supersymmetric solutions of a wide variety of N=1 supergravity
theories coupled to scalar and vector multiplets, including the theory of SU(2)
Yang-Mills coupled to an axion \sigma and dilaton \phi recently obtained as the
reduction to four-dimensions of the six-dimensional Salam-Sezgin model. In this
latter case they provide the most general supersymmetric solution. Passing to
the Riemannian formulation of this theory we show that the most general
supersymmetric solution may be constructed starting from a self-dual Yang-Mills
connection on a self-dual metric and solving a Poisson equation for e^\phi. We
also present the generalization of these solutions to non-Abelian AdS pp-waves
which allow a negative cosmological constant and preserve 1/4 of supersymmetry.Comment: Latex, 1+12 page
The Indefinite Self-Dual Metrics and Painleve Equations
We classify the SU(2)-invariant anti-self-dual metrics with a signature
(+,+,-,-). The metrics are specified by a solution of Painleve VI, V, III or
II. Moreover we show the geometric meaning of the metrics specified by each
type of Painlev\'e functions.Comment: 12 pages, AMS-LaTeX V1.
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