Kleinian Geometry and the N=2 Superstring

This paper is devoted to the exploration of some of the geometrical issues raised by the $N=2$ superstring. We begin by reviewing the reasons that $\beta$-functions for the $N=2$ 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 $\beta$-function equations. Finally we speculate on the deeper significance of some of these spacetimes.Comment: 30 pages, AMS-Te

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

Radiation from Excited Vortex in the Abelian Higgs Model

Excitation of a vortex in the Abelian Higgs model is investigated with the help of a polynomial approximation. The excitation can be regarded as a longitudinal component of the vector field trapped by the vortex. The energy and profile of the excitation are found. Back-reaction of the excitation on the vortex is calculated in the small $\kappa$ limit. It turns out that in the presence of the excitation the vortex effectively becomes much wider - its radius oscillates in time and for all times it is not smaller than the radius of the unexcited vortex. Moreover, we find that the vector field of the excited vortex has long range radiative component. Bound on the amplitude of the excitation is also found.Comment: Latex, 20 pages. 2 figures attached as .uu file to be decoded and used as input for epsfbox command which is already included in the main Latex fil

Statistical Mechanics of Charged Particles in Einstein-Maxwell-Scalar Theory

We consider an $N$-body system of charged particle coupled to gravitational, electromagnetic, and scalar fields. The metric on moduli space for the system can be considered if a relation among the charges and mass is satisfied, which includes the BPS relation for monopoles and the extreme condition for charged black holes. Using the metric on moduli space in the long distance approximation, we study the statistical mechanics of the charged particles at low velocities. The partition function is evaluated as the leading order of the large $d$ expansion, where $d$ is the spatial dimension of the system and will be substituted finally as $d=3$.Comment: 11 pages, RevTeX3.

Vortex Dynamics in Selfdual Maxwell-Higgs Systems with Uniform Background Electric Charge Density

We introduce selfdual Maxwell-Higgs systems with uniform background electric charge density and show that the selfdual equations satisfied by topological vortices can be reduced to the original Bogomol'nyi equations without any background. These vortices are shown to carry no spin but to feel the Magnus force due to the shielding charge carried by the Higgs field. We also study the dynamics of slowly moving vortices and show that the spin-statistics theorem holds to our vortices.Comment: 24 pages + 2 figures ( not included), Cu-TP-611, IASSNS-HEP-93/33, NSF-ITP-93-13

Low energy dynamics of U(1)^{N} Chern-Simons solitons

We apply the adiabatic approximation to investigate the low energy dynamics of vortices in the parity invariant double self-dual Higgs model with only mutual Chern-Simons interaction. When distances between solitons are large they are particles subject to the mutual interaction. The dual formulation of the model is derived to explain the sign of the statistical interaction. When vortices of different types pass one through another they behave like charged particles in magnetic field. They can form a bound state due to the mutual magnetic trapping. Vortices of the same type exhibit no statistical interaction. Their short range interactions are analysed. Possible quantum effects due to the finite width of vortices are discussed.Comment: keywords: vortex, vortices, anyons, fractional statistics, 20 pages in Latex, accepted for publication in Phys.Rev.D, ( the above keywords missing in the title were added

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" $S^1 \times S^2$, or the quotient of $S^3$ 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 $\mathbb R^4,S^2 \times S^2$'s and $CP^2$'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

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