222 research outputs found
Kleinian Geometry and the N=2 Superstring
This paper is devoted to the exploration of some of the geometrical issues
raised by the superstring. We begin by reviewing the reasons that
-functions for the superstring require it to live in a
four-dimensional self-dual spacetime of signature , together with some
of the arguments as to why the only degree of freedom in the theory is that
described by the gravitational field. We then move on to describe at length the
geometry of flat space, and how a real version of twistor theory is relevant to
it. We then describe some of the more complicated spacetimes that satisfy the
-function equations. Finally we speculate on the deeper significance of
some of these spacetimes.Comment: 30 pages, AMS-Te
Low-Energy Dynamics of Supersymmetric Solitons
In bosonic field theories the low-energy scattering of solitons that saturate
Bogomol'nyi-type bounds can be approximated as geodesic motion on the moduli
space of static solutions. In this paper we consider the analogous issue within
the context of supersymmetric field theories. We focus our study on a class of
non-linear sigma models in based on an arbitrary K\"ahler target
manifold and their associated soliton or ``lump" solutions. Using a collective
co-ordinate expansion, we construct an effective action which, upon
quantisation, describes the low-energy dynamics of the lumps. The effective
action is an supersymmetric quantum mechanics action with the target
manifold being the moduli space of static charge lump solutions of the
sigma model. The Hilbert space of states of the effective theory consists of
anti-holomorphic forms on the moduli space. The normalisable elements of the
dolbeault cohomology classes of the moduli space correspond to zero
energy bound states and we argue that such states correpond to bound states in
the full quantum field theory of the sigma model.Comment: 25 page
Low Energy Dynamics of N=2 Supersymmetric Monopoles
It is argued that the low-energy dynamics of monopoles in N=2
supersymmetric Yang-Mills theory are determined by an N=4 supersymmetric
quantum mechanics based on the moduli space of static monople solutions.
This generalises Manton's ``geodesic approximation" for studying the low-energy
dynamics of (bosonic) BPS monopoles. We discuss some aspects of the
quantisation and in particular argue that dolbeault cohomology classes of the
moduli space are related to bound states of the full quantum field theory.Comment: 20 pages, EFI-93-0
Scattering of Macroscopic Heterotic Strings
We show that macroscopic heterotic strings, formulated as strings which wind
around a compact direction of finite but macroscopic extent, exhibit
non-trivial scattering at low energies. This occurs at order velocity squared
and may thus be described as geodesic motion on a moduli space with a
non-trivial metric which we construct. Our result is in agreement with a direct
calculation of the string scattering amplitude.Comment: 14 pp (harvmac l
Uniqueness Theorem of Static Degenerate and Non-degenerate Charged Black Holes in Higher Dimensions
We prove the uniqueness theorem for static higher dimensional charged black
holes spacetime containing an asymptotically flat spacelike hypersurface with
compact interior and with both degenerate and non-degenerate components of the
event horizon.Comment: 9 pages, RevTex, to be published in Phys.Rev.D1
Magnetic bubble refraction and quasibreathers in inhomogeneous antiferromagnets
The dynamics of magnetic bubble solitons in a two-dimensional isotropic
antiferromagnetic spin lattice is studied, in the case where the exchange
integral J(x,y) is position dependent. In the near continuum regime, this
system is described by the relativistic O(3) sigma model on a spacetime with a
spatially inhomogeneous metric, determined by J. The geodesic approximation is
used to describe low energy soliton dynamics in this system: n-soliton motion
is approximated by geodesic motion in the moduli space of static n-solitons,
equipped with the L^2 metric. Explicit formulae for this metric for various
natural choices of J(x,y) are obtained. From these it is shown that single
soliton trajectories experience refraction, with 1/J analogous to the
refractive index, and that this refraction effect allows the construction of
simple bubble lenses and bubble guides. The case where J has a disk
inhomogeneity (taking the value J_1 outside a disk, and J_2<J_1 inside) is
considered in detail. It is argued that, for sufficiently large J_1/J_2 this
type of antiferromagnet supports approximate quasibreathers: two or more
coincident bubbles confined within the disk which spin internally while their
shape undergoes periodic oscillations with a generically incommensurate period.Comment: Conference proceedings paper for talk given at Nonlinear Physics
Theory and Experiment IV, Gallipoli, Italy, June 200
The geodesic approximation for lump dynamics and coercivity of the Hessian for harmonic maps
The most fruitful approach to studying low energy soliton dynamics in field
theories of Bogomol'nyi type is the geodesic approximation of Manton. In the
case of vortices and monopoles, Stuart has obtained rigorous estimates of the
errors in this approximation, and hence proved that it is valid in the low
speed regime. His method employs energy estimates which rely on a key
coercivity property of the Hessian of the energy functional of the theory under
consideration. In this paper we prove an analogous coercivity property for the
Hessian of the energy functional of a general sigma model with compact K\"ahler
domain and target. We go on to prove a continuity property for our result, and
show that, for the CP^1 model on S^2, the Hessian fails to be globally coercive
in the degree 1 sector. We present numerical evidence which suggests that the
Hessian is globally coercive in a certain equivariance class of the degree n
sector for n>1. We also prove that, within the geodesic approximation, a single
CP^1 lump moving on S^2 does not generically travel on a great circle.Comment: 29 pages, 1 figure; typos corrected, references added, expanded
discussion of the main function spac
Towards a classification of static electro-vacuum space-times containing an asymptotically flat spacelike hypersurface with compact interior
We show that static electro-vacuum black hole space-times containing an
asymptotically flat spacelike hypersurface with compact interior and with both
degenerate and non-degenerate components of the event horizon do not exist,
under the supplementary hypothesis that all degenerate components of the event
horizon have charges of the same sign. This extends previous uniqueness
theorems of Simon and Masood-ul-Alam (where only non-degenerate horizons were
allowed) and Heusler (where only degenerate horizons were allowed).Comment: Reverted to original v1; v2 was a result of a manipulation error, and
was meant to be an update to gr-qc/9809088. The problems adressed in the
addendum in v2 of gr-qc/9809088 apply also to this paper, and are similarly
taken care of by the addendum to gr-qc/9809088, and by the analysis in
arXiv:1004.0513 [gr-qc
Enhanced Worldvolume Supersymmetry and Intersecting Domain Walls in N=1 SQCD
We study the worldvolume dynamics of BPS domain walls in N=1 SQCD with N_f=N
flavors, and exhibit an enhancement of supersymmetry for the reduced moduli
space associated with broken flavor symmetries. We provide an explicit
construction of the worldvolume superalgebra which corresponds to an N=2 Kahler
sigma model in 2+1D deformed by a potential, given by the norm squared of a
U(1) Killing vector, resulting from the flavor symmetries broken by unequal
quark masses. This framework leads to a worldvolume description of novel
two-wall junction configurations, which are 1/4-BPS objects, but nonetheless
preserve two supercharges when viewed as kinks on the wall worldvolume.Comment: 35 pages, 3 figures; v2: minor corrections and a reference added, to
appear in Phys. Rev.
Further restrictions on the topology of stationary black holes in five dimensions
We place further restriction on the possible topology of stationary
asymptotically flat vacuum black holes in 5 spacetime dimensions. We prove that
the horizon manifold can be either a connected sum of Lens spaces and "handles"
, or the quotient of by certain finite groups of
isometries (with no "handles"). The resulting horizon topologies include Prism
manifolds and quotients of the Poincare homology sphere. We also show that the
topology of the domain of outer communication is a cartesian product of the
time direction with a finite connected sum of 's
and 's, minus the black hole itself. We do not assume the existence of
any Killing vector beside the asymptotically timelike one required by
definition for stationarity.Comment: LaTex, 22 pages, 9 figure
- …