Supergravity and a Bogomol'nyi Bound in Three Dimensions

We discuss the $2+1$ dimensional Abelian Higgs model coupled to $N=2$ supergravity. We construct the supercharge algebra and, from it, we show that the mass of classical static solutions is bounded from below by the topological charge. As it happens in the global case, half of the supersymmetry is broken when the bound is attained and Bogomol'nyi equations, resulting from the unbroken supersymmetry, hold. These equations, which correspond to gravitating vortices, include a first order self-duality equation whose integrability condition reproduces the Einstein equation.Comment: 25 pages, latex, no figure

Sphalerons, instantons, and standing waves on S3⊗RS^3 \otimes R

We consider pure $SU(2)$ Yang-Mills theory when the space is compactified to a 3-dimensional sphere with finite radius. The Euclidean classical self-dual solutions of the equations of motion (the instantons) and the static finite energy solutions (the sphalerons) which have been found earlier are rewritten in handy physical variables with the gauge condition $A_0 = 0$. Stationary solutions to the equations of motion in the Minkowski space-time (the standing waves) are discussed. We briefly discuss also the theory defined in a flat finite spherical box with rigid boundary conditions and present the numerical solution describing the sphaleron.Comment: LaTeX, 16 pages, 2 figures in a separate uuencoded file. Minor Stylistic revision

The Gravitational Field of String Matter

We study the scattering of a massless and neutral test particle in the gravitational field of a body (the string star) made of a large number of scalar states of the superstring. We consider two cases, the one in which these states are neutral string excitations massive already in ten dimensions and the one in which their masses (and charges) originate in the process of compactification on tori. A perturbative calculation based on superstring amplitudes gives us the deflection angle up to the second order in Newton's constant. A comparison with field theory explicitly shows which among the various massless fields of the superstring give a contribution to the scattering process. In both cases, the deflection angle is smaller than the one computed in general relativity. The perturbative series can be resummed by finding the exact solution to the classical equations of motion of the corresponding low-energy action. The space-time metric of our two examples of string stars has no horizon.Comment: 40 PAGE

Evaporating hydrophilic and superhydrophobic droplets in electric fields

Evaporating water droplets on a heated substrate are investigated in this work. Specifically, the influences of electric fields are studied in the context of the heat flux distribution beneath the droplets as well as the droplet mechanics and resulting shapes and forces. To facilitate a deeper understanding of the problem, both hydrophilic and superhydrophobic droplets are considered for an entire evaporation period with and without electric field effects. Both wetting scenarios show that the net radial directed electric force is directed inward, resulting in a compressive force which influences the droplet shape in such a way that it appears elongated. Conversely, the net vertically directed electric force is determined to be downwardly directed for hydrophilic droplets, pressing the droplet to the surface, whereas it is upwardly directed for the superhydrophobic droplets, representing a lifting force. With regard to the heat transfer to the droplets, only a pronounced electric field effect was observed for the superhydrophobic droplet. For all droplets, the contact line density, representing the ratio of the contact line perimeter to the total base area of the droplet, is determined to be a parameter that unifies the average heat flux from the heater to the droplets. This suggests that the heat transfer to the base of the droplet in the presence of an electric field is dominated by the electric fields influence, or lack thereof, on the contact line density

The anomaly in the central charge of the supersymmetric kink from dimensional regularization and reduction

We show that the anomalous contribution to the central charge of the 1+1-dimensional N=1 supersymmetric kink that is required for BPS saturation at the quantum level can be linked to an analogous term in the extra momentum operator of a 2+1-dimensional kink domain wall with spontaneous parity violation and chiral domain wall fermions. In the quantization of the domain wall, BPS saturation is preserved by nonvanishing quantum corrections to the momentum density in the extra space dimension. Dimensional reduction from 2+1 to 1+1 dimensions preserves the unbroken N=1/2 supersymmetry and turns these parity-violating contributions into the anomaly of the central charge of the supersymmetric kink. On the other hand, standard dimensional regularization by dimensional reduction from 1 to (1-epsilon) spatial dimensions, which also preserves supersymmetry, obtains the anomaly from an evanescent counterterm.Comment: LATeX, 19 pages, v2: significantly extended section 4 on dimensional reduction and evanescent counterterm

Exact Bosonic and Supersymmetric String Black Hole Solutions

We show that Witten's two-dimensional string black hole metric is exactly conformally invariant in the supersymmetric case. We also demonstrate that this metric, together with a recently proposed exact metric for the bosonic case, are respectively consistent with the supersymmetric and bosonic $\sigma$-model conformal invariance conditions up to four-loop order.Comment: 14

Dynamical generation of gauge and Higgs bosons in N=2 supersymmetric non-linear sigma-models

A four-dimensional N=2 supersymmetric non-linear sigma-model with the Eguchi-Hanson (ALE) target space and a non-vanishing central charge is rewritten to a classically equivalent and formally renormalizable gauged `linear' sigma-model over a non-compact coset space in N=2 harmonic superspace by making use of an N=2 vector gauge superfield as the Lagrange multiplier. It is then demonstrated that the N=2 vector gauge multiplet becomes dynamical after taking into account one-loop corrections due to quantized hypermultiplets. This implies the appearance of a composite gauge boson, a composite chiral spinor doublet and a composite complex Higgs particle, all defined as the physical states associated with the propagating N=2 vector gauge superfield. The composite N=2 vector multiplet is further identified with the zero modes of a superstring ending on a D-6-brane. Some non-perturbative phenomena, such as the gauge symmetry enhancement for coincident D-6-branes and the Maldacena conjecture, turn out to be closely related to our NLSM via M-theory. Our results support a conjecture about the composite nature of superstrings ending on D-branes.Comment: 43 pages, LaTeX, 3 figures, macros include

Derivative corrections to D-brane actions with constant background fields

We study derivative corrections to the effective action for a single D-brane in type II superstring theory coupled to constant background fields. In particular, within this setting we determine the complete expression for the (disk level) four-derivative corrections to the Born-Infeld part of the action. We also determine 2n-form 2n-derivative corrections to the Wess-Zumino term. Both types of corrections involve all orders of the gauge field strength, F. The results are obtained via string sigma-model loop calculations using the boundary state operator language. The corrections can be succinctly written in terms of the Riemann tensor for a non-symmetric metric.Comment: 28 pages, LaTeX (uses pstricks); v2: minor typos corrected, references adde

Open-Closed Duality at Tree Level

We study decay of unstable D-branes in string theory in the presence of electric field, and show that the classical open string theory results for various properties of the final state agree with the properties of closed string states into which the system is expected to decay. This suggests a duality between tree level open string theory on unstable D-branes and closed strings at high density.Comment: LaTeX file, 10 page

Conformally rescaled spacetimes and Hawking radiation

We study various derivations of Hawking radiation in conformally rescaled metrics. We focus on two important properties, the location of the horizon under a conformal transformation and its associated temperature. We find that the production of Hawking radiation cannot be associated in all cases to the trapping horizon because its location is not invariant under a conformal transformation. We also find evidence that the temperature of the Hawking radiation should transform simply under a conformal transformation, being invariant for asymptotic observers in the limit that the conformal transformation factor is unity at their location.Comment: 22 pages, version submitted to journa