N=1 de Sitter Supersymmetry Algebra

Recalling the universal covering group of de Sitter, the transformation properties of the spinor fields $\psi(x)$ and ${\bar\psi}(x)$, in the ambient space notation, are presented in this paper. The charge conjugation symmetry of the de Sitter spinor field is then discussed in the above notation. Using this spinor field and charge conjugation, de Sitter supersymmetry algebra in the ambient space notation has been established. It is shown that a novel dS-superalgebra can be attained by the use of spinor field and charge conjugation in the ambient space notation.Comment: 8 pages, LaTeX, some details adde

Scaling of Clusters and Winding Angle Statistics of Iso-height Lines in two-dimensional KPZ Surface

We investigate the statistics of Iso-height lines of (2+1)-dimensional Kardar-Parisi-Zhang model at different level sets around the mean height in the saturation regime. We find that the exponent describing the distribution of the height-cluster size behaves differently for level cuts above and below the mean height, while the fractal dimensions of the height-clusters and their perimeters remain unchanged. The winding angle statistics also confirms again the conformal invariance of these contour lines in the same universality class of self-avoiding random walks (SAWs).Comment: 5 pages, 5 figure

Avalanche frontiers in dissipative abelian sandpile model as off-critical SLE(2)

Avalanche frontiers in Abelian Sandpile Model (ASM) are random simple curves whose continuum limit is known to be a Schramm-Loewner Evolution (SLE) with diffusivity parameter $\kappa = 2$. In this paper we consider the dissipative ASM and study the statistics of the avalanche and wave frontiers for various rates of dissipation. We examine the scaling behavior of a number of functions such as the correlation length, the exponent of distribution function of loop lengths and gyration radius defined for waves and avalanches. We find that they do scale with the rate of dissipation. Two significant length scales are observed. For length scales much smaller than the correlation length, these curves show properties close to the critical curves and the corresponding diffusivity parameter is nearly the same as the critical limit. We interpret this as the ultra violet (UV) limit where $\kappa = 2$ corresponding to $c=-2$. For length scales much larger than the correlation length we find that the avalanche frontiers tend to Self-Avoiding Walk, the corresponding driving function is proportional to the Brownian motion with the diffusion parameter $\kappa =8/3$ corresponding to a field theory with $c = 0$. This is the infra red (IR) limit. Correspondingly the central charge decreases from the IR to the UV point.Comment: 11 Pages, 6 Figure