Massless spinning particle and null-string on AdSdAdS_d: projective-space approach

Massless spinning particle and tensionless string models on $AdS_d$ background in the projective-space realization are proposed as constrained Hamiltonian systems. Various forms of particle and string Lagrangians are derived and classical mechanics is studied including the Lax-type representation of the equations of motion. After that transition to the quantum theory is discussed. Analysis of potential anomalies in the tensionless string model necessitates introduction of ghosts and BRST charge. It is shown that quantum BRST charge is nilpotent for any $d$ if coordinate-momentum ordering for the phase-space bosonic variables, Weyl ordering for the fermions and $cb$ ($\gamma\beta$) ordering for ghosts is chosen, while conformal reparametrizations and space-time dilatations turn out to be anomalous for the ordering in terms of positive and negative Fourier modes of the phase-space variables and ghosts.Comment: 23 pages, v4: In the title and abstract added adjective 'Massless'. In subsection 2.2 the material has been rearranged to streamline the presentation and also a comment added to explain the notation. Minor improvements of the text and further typos corrected. Version accepted for publicatio

Parent formulation at the Lagrangian level

The recently proposed first-order parent formalism at the level of equations of motion is specialized to the case of Lagrangian systems. It is shown that for diffeomorphism-invariant theories the parent formulation takes the form of an AKSZ-type sigma model. The proposed formulation can be also seen as a Lagrangian version of the BV-BRST extension of the Vasiliev unfolded approach. We also discuss its possible interpretation as a multidimensional generalization of the Hamiltonian BFV--BRST formalism. The general construction is illustrated by examples of (parametrized) mechanics, relativistic particle, Yang--Mills theory, and gravity.Comment: 26 pages, discussion of the truncation extended, typos corrected, references adde

The Hidden Convexity of Spectral Clustering

In recent years, spectral clustering has become a standard method for data analysis used in a broad range of applications. In this paper we propose a new class of algorithms for multiway spectral clustering based on optimization of a certain "contrast function" over the unit sphere. These algorithms, partly inspired by certain Independent Component Analysis techniques, are simple, easy to implement and efficient. Geometrically, the proposed algorithms can be interpreted as hidden basis recovery by means of function optimization. We give a complete characterization of the contrast functions admissible for provable basis recovery. We show how these conditions can be interpreted as a "hidden convexity" of our optimization problem on the sphere; interestingly, we use efficient convex maximization rather than the more common convex minimization. We also show encouraging experimental results on real and simulated data.Comment: 22 page

Black Hole Horizons and the Thermodynamics of Strings

We review the classical thermodynamics and the greybody factors of general (rotating) non-extreme black holes and discuss universal features of their near-horizon geometry. We motivate a microscopic interpretation of general black holes that relates the thermodynamics of an effective string theory to the geometry of the black hole in the vicinity of both the outer and the inner event horizons. In this framework we interpret several near-extreme examples, the universal low-energy absorption cross-section, and the emission of higher partial waves from general black holes.Comment: 11 pages, Latex with espcrc2.sty (included); based on talks given at SUSY97 (F.L.) and STRINGS97 (M.C.); Minor correction

Multiple scattering calculations - Geometry for spherical atmospheres

Geometric relationships involved in multiple scattering calculations for spherical planet

Effective Theory on Non-Abelian Vortices in Six Dimensions

Non-Abelian vortices in six spacetime dimensions are obtained for a supersymmetric U(N) gauge theory with N hypermultiplets in the fundamental representation. Massless (moduli) fields are identified and classified into Nambu-Goldstone and quasi-Nambu-Goldstone fields. Effective gauge theories for the moduli fields are constructed on the four-dimensional world volume of vortices. A systematic method to obtain the most general form of the effective Lagrangian consistent with symmetry is proposed. The moduli space for the multi-vortices is found to be a vector bundle over the complex Grassmann manifold.Comment: 30 pages, no figures, typos corrected, references added, the version to appear in Nucl.Phys.