Properties of scalar perturbations generated by conformal scalar field

Primordial scalar perturbations may be generated when complex conformal scalar field rolls down its negative quartic potential. We begin with the discussion of peculiar infrared properties of this scenario. We then consider the statistical anisotropy inherent in the model. Finally, we discuss the non-Gaussianity of scalar perturbations. Because of symmetries, the bispectrum vanishes identically. We present a general expression for the trispectrum and give its explicit form in the folded limit.Comment: Prepared for "Gravity and Cosmology (GC2010)" workshop, Kyoto, Japan, May,24-July,16, 2010; 15 pages, 1 figur

Non-Gaussianity of scalar perturbations generated by conformal mechanisms

We consider theories which explain the flatness of the power spectrum of scalar perturbations in the Universe by conformal invariance, such as conformal rolling model and Galilean Genesis. We show that to the leading {\it non-linear} order, perturbations in all models from this class behave in one and the same way, at least if the energy density of the relevant fields is small compared to the total energy density (spectator approximation). We then turn to the intrinsic non-Gaussianities in these models (as opposed to non-Gaussianities that may be generated during subsequent evolution). The intrinsic bispectrum vanishes, so we perform the complete calculation of the trispectrum and compare it with the trispecta of local forms in various limits. The most peculiar feature of our trispectrum is a (fairly mild) singularity in the limit where two momenta are equal in absolute value and opposite in direction (folded limit). Generically, the intrinsic non-Gaussianity can be of detectable size.Comment: 28 pages, 5 figures. Journal version. A comment on the size of the non-Gaussianities inserted. Misprints corrected. A reference adde

Octonic Electrodynamics

In this paper we present eight-component values "octons", generating associative noncommutative algebra. It is shown that the electromagnetic field in a vacuum can be described by a generalized octonic equation, which leads both to the wave equations for potentials and fields and to the system of Maxwell's equations. The octonic algebra allows one to perform compact combined calculations simultaneously with scalars, vectors, pseudoscalars and pseudovectors. Examples of such calculations are demonstrated by deriving the relations for energy, momentum and Lorentz invariants of the electromagnetic field. The generalized octonic equation for electromagnetic field in a matter is formulated.Comment: 12 pages, 1 figur

Nanopattern-stimulated superconductor-insulator transition in thin TiN films

We present the results of the comparative study of the influence of disorder on transport properties in continuous and nanoperforated TiN films. We show that nanopatterning turns a thin TiN film into an array of superconducting weak links and stimulates both, the disorder- and magnetic field-driven superconductor-to-insulator transitions, pushing them to lower degree of disorder. We find that nanopatterning enhances the role of the two-dimensional Coulomb interaction in the system transforming the originally insulating film into a more pronounced insulator. We observe magnetoresistance oscillations reflecting collective behaviour of the multiconnected nanopatterned superconducting film in the wide range of temperatures and uncover the physical mechanism of these oscillations as phase slips in superconducting weak link network.Comment: 6 pages, 4 figure

On some algebraic examples of Frobenius manifolds

We construct some explicit quasihomogeneous algebraic solutions to the associativity (WDVV) equations by using analytical methods of the finite gap integration theory. These solutions are expanded in the uniform way to non-semisimple Frobenius manifolds.Comment: 14 page

Parafermionic Liouville field theory and instantons on ALE spaces

In this paper we study the correspondence between the $\hat{\textrm{su}}(n)_{k}\oplus \hat{\textrm{su}}(n)_{p}/\hat{\textrm{su}}(n)_{k+p}$ coset conformal field theories and $\mathcal{N}=2$ SU(n) gauge theories on $\mathbb{R}^{4}/\mathbb{Z}_{p}$. Namely we check the correspondence between the SU(2) Nekrasov partition function on $\mathbb{R}^{4}/\mathbb{Z}_{4}$ and the conformal blocks of the $S_{3}$ parafermion algebra (in $S$ and $D$ modules). We find that they are equal up to the U(1)-factor as it was in all cases of AGT-like relations. Studying the structure of the instanton partition function on $\mathbb{R}^4/\mathbb{Z}_p$ we also find some evidence that this correspondence with arbitrary $p$ takes place up to the U(1)-factor.Comment: 21 pages, 6 figures, misprints corrected, references added, version to appear in JHE

A New Feather Mite Species of the Genus \u3ci\u3eTrouessartia\u3c/i\u3e Canestrini (Acariformes: Trouessartiidae) from the Northern Rough-winged Swallow \u3ci\u3eStelgidopteryx serripennis\u3c/i\u3e (Passeriformes: Hirundinidae) in Pennsylvania

A new feather mite species, Trouessartia stelgidopteryx sp. n. (Astigmata: Trouessartiidae), is described from the Northern rough-winged swallow Stelgidopteryx serripennis Newton (Passeriformes: Hirundinidae) in Pennsylvania, USA. The new species is close to the minutipes species group and differs from its representatives and all other known species of the genus Trouessartia in having a unique combination of features in males: the opisthosomal lobes are much longer than wide, they are separated by a large semi-ovate terminal cleft, and their lobar apices bear semi-ovate terminal lamellae with a smooth margin