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

Bounds on the number of connected components for tropical prevarieties

For a tropical prevariety in Rn given by a system of k tropical polynomials in n variables with degrees at most d, we prove that its number of connected components is less than k+7n−

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

Effect of Matter Motion and Polarization in Neutrino Flavour Oscillations

The Lorentz invariant formalism for description of neutrino flavor oscillation in moving and polarized matter is developed. It is shown that the neutrino effective potential, which determines the effective mass difference between neutrinos in matter can be sufficiently changed by relativistic motion of matter. In the case of matter motion parallel to neutrino propagation, matter effects in neutrino flavor oscillations are suppressed. In the case of relativistic motion of matter in the opposite direction sufficient increase of effects of matter in neutrino oscillations is predicted. The dependence of the matter term in neutrino effective potential on the values and correlations of the three vectors, the neutrino and matter speeds and matter polarization, is discussed in details