Ricci-flat spacetimes with l-conformal Galilei symmetry

Ricci-flat metrics of the ultrahyperbolic signature which enjoy the l-conformal Galilei symmetry are constructed. They involve the AdS_2-metric in a way similar to the near horizon black hole geometries. The associated geodesic equations are shown to describe a second order dynamical system for which the acceleration generators are functionally independent.Comment: V2: refs. added, the version to appear in PL

A linear realization for the new space-time superalgebras in ten and eleven dimensions

The new extensions of the Poincar\'e superalgebra recently found in ten and eleven dimensions are shown to admit a linear realization. The generators of the nonlinear and linear group transformations are shown to fall into equivalent representations of the superalgebra. The parametrization of the coset space $G/H$, with $G$ a given extended supergroup and $H$ the Lorentz subgroup, that corresponds to the linear transformations is presented.Comment: 15 pages, LaTe

On the complex structure in the Gupta-Bleuler quantization method

We examine the general conditions for the existence of the complex structure intrinsic in the Gupta-Bleuler quantization method for the specific case of mixed first and second class fermionic constraints in an arbitrary space-time dimension. The cases d=3 and 10 are shown to be of prime importance. The explicit solution for d=10 is presented.Comment: 12 pages, LaTe

Covariant Supplementation Scheme for Infinitely Reducible First Class Constraints

For a rather broad class of dynamical systems subject to mixed fermionic first and second class constraints or infinitely reducible first class constraints (IR1C), a manifestly covariant scheme of supplementation of IR1C to irreducible ones is proposed. For a model with IR1C only, an application of the scheme leads to a system with covariantly splitted and irreducible first and second class constraints. Modified Lagrangian formulations for the Green--Schwarz superstring, Casalbuoni--Brink--Schwarz superparticle and Siegel superparticle, which reproduce the supplementation scheme, are suggested

N=4 mechanics, WDVV equations and roots

N=4 superconformal multi-particle quantum mechanics on the real line is governed by two prepotentials, U and F, which obey a system of partial differential equations linear in U and generalizing the Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equation for F. Putting U=0 yields a class of models (with zero central charge) which are encoded by the finite Coxeter root systems. We extend these WDVV solutions F in two ways: the A_n system is deformed n-parametrically to the edge set of a general orthocentric n-simplex, and the BCF-type systems form one-parameter families. A classification strategy is proposed. A nonzero central charge requires turning on U in a given F background, which we show is outside of reach of the standard root-system ansatz for indecomposable systems of more than three particles. In the three-body case, however, this ansatz can be generalized to establish a series of nontrivial models based on the dihedral groups I_2(p), which are permutation symmetric if 3 divides p. We explicitly present their full prepotentials.Comment: 1+25 pages; v2: major revision (more general analysis, new solutions, additional references); v3: improvements in sects.5,8,9, refs. adde

Quantum mechanics of superparticle with 1/4 supersymmetry breaking

We study quantum mechanics of a massive superparticle in d=4 which preserves 1/4 of the target space supersymmetry with eight supercharges, and so corresponds to the partial breaking N=8 down to N=2. Its worldline action contains a Wess-Zumino term, explicitly breaks d=4 Lorentz symmetry and exhibits one complex fermionic kappa-symmetry. We perform the Hamiltonian analysis of the model and quantize it in two different ways, with gauge-fixed kappa-symmetry and in the Gupta-Bleuler formalism. Both approaches give rise to the same supermultiplet structure of the space of states. It contains three irreducible N=2 multiplets with the total number of (4+4) complex on-shell components. These states prove to be in one-to-one correspondence with the de Rham complex of p-forms on a three-dimensional subspace of the target x-manifold. We analyze the vacuum structure of the model and find that the non-trivial vacua are given by the exact harmonic one- and two-forms. Despite the explicit breaking of the d=4 Lorentz symmetry in the fermionic sector, the d=4 mass-shell condition is still valid in the model.Comment: 20 pages, LaTex, no figure

Conformal Newton–Hooke symmetry of Pais–Uhlenbeck oscillator

K.A. and J.G. are grateful to Piotr Kosiński for helpful and illuminating discussions. We thank Peter Horváthy and Andrei Smilga for useful correspondence. This work was sup-ported by the NCN grant DEC-2013/09/B/ST2/02205 (K.A. and J.G.) and by the RFBR grants 13-02-90602-Arm (A.G.) and 14-02-31139-Mol (I.M.) as well as by the MSU program “Nauka” under the project 825 (A.G. and I.M.). I.M. gratefully acknowledges the support of the Dynasty Foundation. ©2014 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/3.0/). Funded by SCOAP3.It is demonstrated that the Pais–Uhlenbeck oscillator in arbitrary dimension enjoys the l -conformal Newton–Hooke symmetry provided frequencies of oscillation form the arithmetic sequence ωk=(2k−1)ω1, where k=1,…,n, and l is the half-integer View the MathML source. The model is shown to be maximally superintegrable. A link to n decoupled isotropic oscillators is discussed and an interplay between the l-conformal Newton–Hooke symmetry and symmetries characterizing each individual isotropic oscillator is analyzed.This work was sup-ported by the NCN grant DEC-2013/09/B/ST2/02205 (K.A. and J.G.) and by the RFBR grants 13-02-90602-Arm (A.G.) and 14-02-31139-Mol (I.M.) as well as by the MSU program “Nauka” under the project 825 (A.G. and I.M.). I.M. gratefully acknowledges the support of the Dynasty Foundation