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

Unfolding Mixed-Symmetry Fields in AdS and the BMV Conjecture: I. General Formalism

We present some generalities of unfolded on-shell dynamics that are useful in analysing the BMV conjecture for mixed-symmetry fields in constantly curved backgrounds. In particular we classify the Lorentz-covariant Harish-Chandra modules generated from primary Weyl tensors of arbitrary mass and shape, and in backgrounds with general values of the cosmological constant. We also discuss the unfolded notion of local degrees of freedom in theories with and without gravity and with and without massive deformation parameters, using the language of Weyl zero-form modules and their duals.Comment: Corrected typos, references added, two figures, some remarks and two subsections added for clarit

Higher Spin Gravity with Matter in AdS_3 and Its CFT Dual

We study Vasiliev's system of higher spin gauge fields coupled to massive scalars in AdS_3, and compute the tree level two and three point functions. These are compared to the large N limit of the W_N minimal model, and nontrivial agreements are found. We propose a modified version of the conjecture of Gaberdiel and Gopakumar, under which the bulk theory is perturbatively dual to a subsector of the CFT that closes on the sphere.Comment: 58 pages; typos corrected, references adde

Metastable and stable equilibrium states of stellar electron-nuclear plasmas

By minimizing free energy density, we show that the stellar core of a hydrogen burning star is not in a global thermodynamical equilibrium unless density, temperature, mass and composition assume given values. The core (as the solar interior) may be viewed more appropriately as a metastable state with very long lifetime. Slightly non-extensive distribution function could be the natural distribution for a weakly non-ideal plasma like a stellar core and represents a more appropriate approximation to this system than a Maxwellian distribution, without affecting bulk properties of stars.Comment: 14 pages, to appear in Phys. Lett.

On the relation between local and geometric Lagrangians for higher spins

Equations of motion for free higher-spin gauge fields of any symmetry can be formulated in terms of linearised curvatures. On the other hand, gauge invariance alone does not fix the form of the corresponding actions which, in addition, either contain higher derivatives or involve inverse powers of the d'Alembertian operator, thus introducing possible subtleties in degrees of freedom count. We suggest a path to avoid ambiguities, starting from local, unconstrained Lagrangians previously proposed, and integrating out the auxiliary fields from the functional integral, thus generating a unique non-local theory expressed in terms of curvatures.Comment: 14 pages. Contribution to the proceedings of the 1st Mediterranean Conference on Classical and Quantum Gravity, Kolymbary (Crete, Greece) September 14-18 200

A magneto-gravitational trap for precision studies of gravitational quantum states

Observation time is the key parameter for improving the precision of measurements of gravitational quantum states of particles levitating above a reflecting surface. We propose a new method of long confinement in such states of atoms, anti-atoms, neutrons and other particles possessing a magnetic moment. The Earth gravitational field and a reflecting mirror confine particles in the vertical direction. The magnetic field originating from electric current passing through a vertical wire confines particles in the radial direction. Under appropriate conditions, motions along these two directions are decoupled to a high degree. We estimate characteristic parameters of the problem, and list possible systematic effects that limit storage times due to the coupling of the two motions. In the limit of low particle velocities and magnetic fields, precise control of the particle motion and long storage times in the trap can provide ideal conditions for both gravitational, optical and hyperfine spectroscopy: for the sensitive verification of the equivalence principle for antihydrogen atoms; for increasing the accuracy of optical and hyperfine spectroscopy of atoms and antiatoms; for improving constraints on extra fundamental interactions from experiments with neutrons, atoms and antiatoms

Spin Evolution of Supermassive Black Holes and Galactic Nuclei

The spin angular momentum S of a supermassive black hole (SBH) precesses due to torques from orbiting stars, and the stellar orbits precess due to dragging of inertial frames by the spinning hole. We solve the coupled post-Newtonian equations describing the joint evolution of S and the stellar angular momenta Lj, j = 1...N in spherical, rotating nuclear star clusters. In the absence of gravitational interactions between the stars, two evolutionary modes are found: (1) nearly uniform precession of S about the total angular momentum vector of the system; (2) damped precession, leading, in less than one precessional period, to alignment of S with the angular momentum of the rotating cluster. Beyond a certain distance from the SBH, the time scale for angular momentum changes due to gravitational encounters between the stars is shorter than spin-orbit precession times. We present a model, based on the Ornstein-Uhlenbeck equation, for the stochastic evolution of star clusters due to gravitational encounters and use it to evaluate the evolution of S in nuclei where changes in the Lj are due to frame dragging close to the SBH and to encounters farther out. Long-term evolution in this case is well described as uniform precession of the SBH about the cluster's rotational axis, with an increasingly important stochastic contribution when SBH masses are small. Spin precessional periods are predicted to be strongly dependent on nuclear properties, but typical values are 10-100 Myr for low-mass SBHs in dense nuclei, 100 Myr - 10 Gyr for intermediate mass SBHs, and > 10 Gyr for the most massive SBHs. We compare the evolution of SBH spins in stellar nuclei to the case of torquing by an inclined, gaseous accretion disk.Comment: 25 page

Conformal self-dual fields

Conformal self-dual fields in flat space-time of even dimension greater than or equal to four are studied. Ordinary-derivative formulation of such fields is developed. Gauge invariant Lagrangian with conventional kinetic terms and corresponding gauge transformations are obtained. Gauge symmetries are realized by involving the Stueckelberg fields. Realization of global conformal symmetries is obtained. Light-cone gauge Lagrangian is found. Also, we demonstrate use of the light-cone gauge for counting of on-shell degrees of freedom of the conformal self-dual fields.Comment: 28 pages, LaTeX-2e, v3: Discussion of realization of conformal algebra symmetries on field strengths added to Sections 3,5. Appendices B,C,D and one reference added. Typos correcte

Universality in nonadiabatic behaviour of classical actions in nonlinear models with separatrix crossings

We discuss dynamics of approximate adiabatic invariants in several nonlinear models being related to physics of Bose-Einstein condensates (BEC). We show that nonadiabatic dynamics in Feshbach resonance passage, nonlinear Landau-Zener (NLZ) tunnelling, and BEC tunnelling oscillations in a double-well can be considered within a unifying approach based on the theory of separatrix crossings. The separatrix crossing theory was applied previously to some problems of classical mechanics, plasma physics and hydrodynamics, but has not been used in the rapidly growing BEC-related field yet. We derive explicit formulas for the change in the action in several models. Extensive numerical calculations support the theory and demonstrate its universal character. We also discovered a qualitatively new nonlinear phenomenon in a NLZ model which we propose to call {\em separated adiabatic tunnelling}Comment: Accepted for publication in Physical Review E; Several misprints are corrected; main results are emphasized in the end of Introduction (including finite conversion efficiency in Feshbach resonance passage due to geometric jump in the action); bibliography is extende