Anton Galajinsky

Quartet unconstrained formulation for massless higher spin fields

We construct simple unconstrained Lagrangian formulations for massless higher spin fields in flat space of arbitrary dimension and on anti-de Sitter background. Starting from the triplet equations of Francia and Sagnotti, which describe a chain of spin modes, we introduce an auxiliary field and find appropriate gauge invariant constraints that single out the spin-s mode. The resulting quartet of fields, thus describing an irreducible representation of the Poincare group, is used to construct simple Lagrangian formulations, which are local, free from higher derivative terms and use equal number of auxiliary fields for an unconstrained description of any value of spin. Our method proves to be most efficient for an unconstrained description of massless higher spin fermions in anti-de Sitter space. A relation of the minimal models with the universal BRST approach is discussed.

AdS2/CFT1, canonical transformations and superconformal mechanics

Abstract We propose a simple conformal mechanics model which is classically equivalent to a charged massive particle propagating near the AdS2×S2 horizon of an extreme Reissner–Nordstrom black hole. The equivalence holds for any finite value of the black hole mass and with both the radial and angular degrees of freedom of the particle taken into account. It is ensured by the existence of a canonical transformation in the Hamiltonian formalism. Using this transformation, we construct the Hamiltonian of a N=4 superparticle on AdS2×S2 background.

4 superconformal Calogero models

We continue the research initiated in hep-th/0607215 and apply our method of conformal automorphisms to generate various = 4 superconformal quantum many-body systems on the real line from a set of decoupled particles extended by fermionic degrees of freedom. The {su}(1,1|2) invariant models are governed by two scalar potentials obeying a system of nonlinear partial differential equations which generalizes the Witten-Dijkgraaf-Verlinde-Verlinde equations. As an application, the = 4 superconformal extension of the three-particle (A-type) Calogero model generates a unique G2-type Hamiltonian featuring three-body interactions. We fully analyze the = 4 superconformal three- and four-particle models based on the root systems of A1⊕G2 and F4, respectively. Beyond Wyllards solutions we find a list of new models, whose translational non-invariance of the center-of-mass motion fails to decouple and extends even to the relative particle motion.

Conformal mechanics in Newton–Hooke spacetime

Conformal many–body mechanics in Newton–Hooke spacetime is studied within the framework of the Lagrangian formalism. Global symmetries and Noether charges are given in a form convenient for analyzing the flat space limit. N = 2 superconformal extension is built and a new class on N = 2 models related to simple Lie algebras is presented. A decoupling similarity transformation on N = 2 quantum mechanics in Newton–Hooke spacetime is discussed.

Particle dynamics near extreme Kerr throat and supersymmetry

The extreme Kerr throat solution is believed to be non-supersymmetric. However, its isometry group SO(2, 1) × U(1) matches precisely the bosonic subgroup of

Remarks on l-conformal extension of the Newton–Hooke algebra

\mathcal{N} = 2

N=4 mechanics, WDVV equations and roots

superconformal group in one dimension. In this paper we construct

Remark on quantum mechanics with conformal Galilean symmetry

\mathcal{N} = 2

Dynamical realizations of l-conformal Newton–Hooke group

supersymmetric extension of a massive particle moving near the horizon of the extreme Kerr black hole. Bosonic conserved charges are related to Killing vectors in a conventional way. Geometric interpretation of supersymmetry charges remains a challenge.

Particle dynamics on AdS(2) x S**2 background with two-form flux

Abstract The l -conformal extension of the Newton–Hooke algebra proposed in [J. Negro, M.A. del Olmo, A. Rodriguez-Marco, J. Math. Phys. 38 (1997) 3810] is formulated in the basis in which the flat space limit is unambiguous. Admissible central charges are specified. The infinite-dimensional Virasoro–Kac–Moody type extension is given.