Dual Actions for Born-Infeld and Dp-Brane Theories

Dual actions with respect to U(1) gauge fields for Born-Infeld and $Dp$-brane theories are reexamined. Taking into account an additional condition, i.e. a corollary to the field equation of the auxiliary metric, one obtains an alternative dual action that does not involve the infinite power series in the auxiliary metric given by ref. \cite{s14}, but just picks out the first term from the series formally. New effective interactions of the theories are revealed. That is, the new dual action gives rise to an effective interaction in terms of one interaction term rather than infinite terms of different (higher) orders of interactions physically. However, the price paid for eliminating the infinite power series is that the new action is not quadratic but highly nonlinear in the Hodge dual of a $(p-1)$-form field strength. This non-linearity is inevitable to the requirement the two dual actions are equivalent.Comment: v1: 11 pages, no figures; v2: explanation of effective interactions added; v3: concision made; v4: minor modification mad

Duality Symmetry in Momentum Frame

Siegel's action is generalized to the D=2(p+1) (p even) dimensional space-time. The investigation of self-duality of chiral p-forms is extended to the momentum frame, using Siegel's action of chiral bosons in two space-time dimensions and its generalization in higher dimensions as examples. The whole procedure of investigation is realized in the momentum space which relates to the configuration space through the Fourier transformation of fields. These actions correspond to non-local Lagrangians in the momentum frame. The self-duality of them with respect to dualization of chiral fields is uncovered. The relationship between two self-dual tensors in momentum space, whose similar form appears in configuration space, plays an important role in the calculation, that is, its application realizes solving algebraically an integral equation.Comment: 11 pages, no figures, to appear in Phys. Rev.

On a Localized Riemannian Penrose Inequality

Consider a compact, orientable, three dimensional Riemannian manifold with boundary with nonnegative scalar curvature. Suppose its boundary is the disjoint union of two pieces: the horizon boundary and the outer boundary, where the horizon boundary consists of the unique closed minimal surfaces in the manifold and the outer boundary is metrically a round sphere. We obtain an inequality relating the area of the horizon boundary to the area and the total mean curvature of the outer boundary. Such a manifold may be thought as a region, surrounding the outermost apparent horizons of black holes, in a time-symmetric slice of a space-time in the context of general relativity. The inequality we establish has close ties with the Riemannian Penrose Inequality, proved by Huisken and Ilmanen, and by Bray.Comment: 16 page

Quantisation of 2D-gravity with Weyl and area-preserving diffeomorphism invariances

The constraint structure of 2D-gravity with the Weyl and area-preserving diffeomorphism invariances is analysed in the ADM formulation. It is found that when the area-preserving diffeomorphism constraints are kept, the usual conformal gauge does not exist, whereas there is the possibility to choose the so-called ``quasi-light-cone'' gauge, in which besides the area-preserving diffeomorphism invariance, the reduced Lagrangian also possesses the SL(2,R) residual symmetry. The string-like approach is applied to quantise this model, but a fictitious non-zero central charge in the Virasoro algebra appears. When a set of gauge-independent SL(2,R) current-like fields is introduced instead of the string-like variables, a consistent quantum theory is obtained.Comment: 14 pages, Latex fil

On the volume functional of compact manifolds with boundary with constant scalar curvature

We study the volume functional on the space of constant scalar curvature metrics with a prescribed boundary metric. We derive a sufficient and necessary condition for a metric to be a critical point, and show that the only domains in space forms, on which the standard metrics are critical points, are geodesic balls. In the zero scalar curvature case, assuming the boundary can be isometrically embedded in the Euclidean space as a compact strictly convex hypersurface, we show that the volume of a critical point is always no less than the Euclidean volume bounded by the isometric embedding of the boundary, and the two volumes are equal if and only if the critical point is isometric to a standard Euclidean ball. We also derive a second variation formula and apply it to show that, on Euclidean balls and ''small'' hyperbolic and spherical balls in dimensions 3 to 5, the standard space form metrics are indeed saddle points for the volume functional

Enhanced spin-orbit torques in MnAl/Ta films with improving chemical ordering

We report the enhancement of spin-orbit torques in MnAl/Ta films with improving chemical ordering through annealing. The switching current density is increased due to enhanced saturation magnetization MS and effective anisotropy field HK after annealing. Both damplinglike effective field HD and fieldlike effective field HF have been increased in the temperature range of 50 to 300 K. HD varies inversely with MS in both of the films, while the HF becomes liner dependent on 1/MS in the annealed film. We infer that the improved chemical ordering has enhanced the interfacial spin transparency and the transmitting of the spin current in MnAl layer

Critical points of Wang-Yau quasi-local energy

In this paper, we prove the following theorem regarding the Wang-Yau quasi-local energy of a spacelike two-surface in a spacetime: Let $\Sigma$ be a boundary component of some compact, time-symmetric, spacelike hypersurface $\Omega$ in a time-oriented spacetime $N$ satisfying the dominant energy condition. Suppose the induced metric on $\Sigma$ has positive Gaussian curvature and all boundary components of $\Omega$ have positive mean curvature. Suppose $H \le H_0$ where $H$ is the mean curvature of $\Sigma$ in $\Omega$ and $H_0$ is the mean curvature of $\Sigma$ when isometrically embedded in $R^3$. If $\Omega$ is not isometric to a domain in $R^3$, then 1. the Brown-York mass of $\Sigma$ in $\Omega$ is a strict local minimum of the Wang-Yau quasi-local energy of $\Sigma$, 2. on a small perturbation $\tilde{\Sigma}$ of $\Sigma$ in $N$, there exists a critical point of the Wang-Yau quasi-local energy of $\tilde{\Sigma}$.Comment: substantially revised, main theorem replaced, Section 3 adde