Pohlmeyer reduction of AdS_5 x S^5 superstring sigma model

Motivated by a desire to find a useful 2d Lorentz-invariant reformulation of the AdS_5 x S^5 superstring world-sheet theory in terms of physical degrees of freedom we construct the Pohlmeyer-reduced version of the corresponding sigma model. The Pohlmeyer reduction procedure involves several steps. Starting with a coset space string sigma model in the conformal gauge and writing the classical equations in terms of currents one can fix the residual conformal diffeomorphism symmetry and kappa-symmetry and introduce a new set of variables (related locally to currents but non-locally to the original string coordinate fields) so that the Virasoro constraints are automatically satisfied. The resulting gauge-fixed equations can be obtained from a Lagrangian of a non-abelian Toda type: a gauged WZW model with an integrable potential coupled also to a set of 2d fermionic fields. A gauge-fixed form of the Pohlmeyer-reduced theory can be found by integrating out the 2d gauge field of the gauged WZW model. Its small-fluctuation spectrum contains 8 bosonic and 8 fermionic degrees of freedom with equal masses. We conjecture that the reduced model has world-sheet supersymmetry and is ultraviolet-finite. We show that in the special case of the AdS_2 x S^2 superstring model the reduced theory is indeed supersymmetric: it is equivalent to the N=2 supersymmetric extension of the sine-Gordon model.Comment: 56 pages. v2: section 6.4 expanded with comments on mass spectrum and the corresponding S-matrix; v3,v4: minor corrections and clarifications adde

On conformal higher spins in curved background

We address the question of how to represent an interacting action for the tower of conformal higher spin fields in a form covariant with respect to a background metric. We use a background metric to define a star product which plays a central role in the definition of the corresponding gauge transformations. By an analogy with the kinetic term in the 4-derivative Weyl gravity action expanded near an on-shell background one expects that the kinetic term in such an action should be gauge-invariant in a Bach-flat metric. We demonstrate this fact to first order in expansion in powers of the curvature of the background metric. This generalizes the result of arXiv:1404.7452 for spin 3 case to all conformal higher spins. We also comment on a possibility of extending this claim to terms quadratic in the curvature and discuss the appearance of background-dependent mixing terms in the quadratic part of the conformal higher spin action.Comment: 24 pages. v2,v3: minor corrections and remarks adde

BRST-anti-BRST Symmetric Conversion of Second-Class Constraints

A general method of the BRST--anti-BRST symmetric conversion of second-class constraints is presented. It yields a pair of commuting and nilpotent BRST-type charges that can be naturally regarded as BRST and anti-BRST ones. Interchanging the BRST and anti-BRST generators corresponds to a symmetry between the original second-class constraints and the conversion variables, which enter the formalism on equal footing.Comment: 12 pages, misprints correcte

Charged complexes at the surface of liquid helium

Charged clusters in liquid helium in an external electric field form a two-dimensional system below the helium surface. This 2D system undergoes a phase transition from a liquid to a Wigner crystal at rather high temperatures. Contrary to the electron Wigner crystal, the Wigner lattice of charged clusters can be detected directly.Comment: 6 pages, 1 figur