Tachyon solution in a cubic Neveu-Schwarz string field theory

We find a class of analytic solutions in a modified cubic theory of fermionic strings that includes the GSO(−) sector. This class contains a solution that involves a tachyon field from the GSO(−) sector and reproduces the correct value of the non-BPS D-brane tension. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 158, No. 3, pp. 378–390, March, 2009.     

Iterative method for solving nonlinear integral equations describing rolling solutions in string theory

We consider a nonlinear integral equation with infinitely many derivatives that appears when a system of interacting open and closed strings is investigated if the nonlocality in the closed string sector is neglected. We investigate the properties of this equation, construct an iterative method for solving it, and prove that the method converges. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 146, No. 3, pp. 402–409, March, 2006.     

Pure gauge configurations and tachyon solutions for cubic fermionic string field theory equations of motion

Special perturbative pure gauge solutions parameterized by a pair of wedge states are parts of the nontrivial (not purely gauge) tachyon solutions of the cubic fermionic string field theory describing the non-BPS brane true vacuum. We demonstrate explicitly that for the large parameter of the perturbation expansion, these pure gauge configurations are no longer solutions of the equations of motion. We show that this problem is solved by adding an extra term that is just the term needed for the first Sen conjecture to hold.     

Integrable structure of the field theory of open superstrings

We find asymptotic expansions in the “string mass” μ for μ-deformed Γ-functions and Neumann coefficients characterizing the three-string vertex in the light-cone gauge of the field theory of open superstrings on a maximally supersymmetric pp-wave background. Dedicated to the 80th birthday of Academician Anatolii Alekseevich Logunov __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 149, No. 3, pp. 381–385, December, 2006.     

Multipoint correlation functions in Liouville field theory and minimal Liouville gravity

We study (n+3)-point correlation functions of exponential fields in the Liouville field theory with n degenerate and three arbitrary fields and derive an analytic expression for these correlation functions in terms of Coulomb integrals. We consider the application of these results to the minimal Liouville gravity. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 3, pp. 536–556, March, 2008.     

Scattering theory for a class of fermionic Pauli-Fierz models

The scattering theory for a class of fermionic Pauli-Fierz models is considered. We give a proof of the asymptotic completeness of the dynamics in the case of massive fermions. The result applied to the Hamiltonian of a quantized spin- Dirac particle interacting with an external field through a cutoff Yukawa interaction and to the Hamiltonian of a system of finitely many confined particles coupled to a fermionic field with a quadratic interaction.     

Electrically charged solitons in gauge field theory

Monopoles and vortices are well known magnetically charged soliton solutions of gauge field equations. Extending the idea of Dirac on monopoles, Schwinger pioneered the concept of solitons carrying both electric and magnetic charges, called dyons, which are useful in modeling elementary particles. Mathematically, the existence of dyons presents interesting variational partial differential equation problems, subject to topological constraints. This article is a survey on recent progress in the study of dyons.     

Multidimensional basis of p-adic wavelets and representation theory

A multidimensional basis of p-adic wavelets is constructed. The relation of the constructed basis to a system of coherent states i.e., orbit of action) for some p-adic group of linear transformations is discussed. We show that the set of products of the vectors from the constructed basis and p-roots of unity is the orbit of the corresponding p-adic group of linear transformations. The text was submitted by the authors in English.     

Jost-Lehmann-Dyson representation,analyticity in the angular variable,and upper bounds in noncommutative quantum field theory

We prove the existence of an analogue of the Jost-Lehmann-Dyson representation in noncommutative quantum field theory for the case where the noncommutativity affects only the spatial variables. Using this representation, we show that there is a certain class of elastic scattering amplitudes that have an analytic continuation to the complex cos plane with the Martin ellipse as the related analyticity domain. Using the analyticity in the angular variable and the unitarity as a basis, we establish an analogue of the Froissart—Martin bound for the total cross section in the noncommutative case.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 2, pp. 388–403, February, 2005.     

Exact solution in a string cosmological model

We construct an exact solution of the Friedmann equations with a phantom scalar matter field originating in string field theory and show the absence of the big-rip singularity. The notable features of the model are a ghost sign of the kinetic term and a special polynomial form of the effective tachyon potential. The constructed solution is stable under small fluctuations of the initial conditions and special variations of the form of the potential. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 148, No. 1, pp. 23–41, July, 2006. An erratum to this article is available at .     

Construction of exact solutions in two-field cosmological models

We construct a dark energy model with a phantom scalar field, a standard scalar field, and a polynomial potential inspired by string field theory. We find a two-parameter set of exact solutions of the Friedmann equations. We find a potential satisfying the conditions obtained from the string theory and such that at large times, some of the exact solutions correspond to the state parameter w_DE > −1 while the others correspond to w_DE < −1. We demonstrate that the superpotential method is very effective for seeking new exact solutions. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 1, pp. 47–61, April, 2008.     

Partition functions of matrix models as the first special functions of string theory: Finite Hermitian one-matrix model

Although matrix model partition functions do not exhaust the entire set of -functions relevant for string theory, they are elementary blocks for constructing many other -functions and seem to capture the fundamental nature of quantum gravity an string theory properly. We propose taking matrix model partition functions as new special functions. This means that they should be investigated and represented in some standard form without reference to particular applications. At the same time, the tables and lists of properties should be sufficiently full to exclude unexpected peculiarities appearing in new applications. Accomplishing this task requires considerable effort, and this paper is only a first step in this direction. We restrict our consideration to the finite Hermitian one-matrix model an concentrate mostly on its phase and branch structure that arises when the partition function is considered as a D-module. We discuss the role of the CIV-DV prepotential (which generates a certain basis in the linear space of solutions of the Virasoro constraints, although an understanding of why and how this basis is distinguished is lacking) an evaluate several first multiloop correlators, which generalize the semicircular distribution to the case of multitrace and nonplanar correlators.Translated from Teoreticheskaya i Matematicheskaya Fizika,Vol. 142, No. 3, pp. 419–488, March, 2005.     

On the product of vector spaces in a commutative field extension

Let K⊂L be a commutative field extension. Given K-subspaces A,B of L, we consider the subspace 〈AB〉 spanned by the product set . If dimKA=r and dimKB=s, how small can the dimension of 〈AB〉 be? In this paper we give a complete answer to this question in characteristic 0, and more generally for separable extensions. The optimal lower bound on dimK〈AB〉 turns out, in this case, to be provided by the numerical function

     

A globally convergent method for computing multiple vortices in a supersymmetric field theory

Computation of the solutions to the gauge field equations is known of great importance for the simulation of various particle physics systems. In this work, we establish a globally convergent iterative method for computing the multiple vortex solutions arising in a self-dual system of non-Abelian gauge field equations derived in a supersymmetric theory model. Using this method, we present a few numerical examples which demonstrate the effectiveness of the method and, at the same time, provide a concrete realization of the soliton-like behavior of the vortexlines concentrated around centers of vortices, which is believed to be essential for linear confinement in QCD.     

Integral representation in the theory of continuous trading

This paper deals with predictable representation in continuous trading. First of all we give a positive answer to a conjecture of Harrison and Pliska [2]. Then we prove the completeness of a model of mixed type (see[2]). A slight modificationof this example shows that the continuous and purely discontinuous parts of a local martingale depend on the filtration.     

Cohomology of elementary states in twistor conformal field theory

In Twistor Conformal Field Theory the Riemann surfaces and holomorphic functions of two-dimensional conformal field theory are replaced by flat twistor spaces (arising from conformally-flat four-manifolds) and elements of the holomorphic first cohomology. The analogue of a Laurent Series is the expansion of a cohomology element in elementary states and we calculate the dimension of the space of these states for twistor spaces of compact hyperbolic manifolds. Our method follows the strategy used in the classical problem of calculating the number of meromorphic functions with prescribed poles on Rieiemann surface. We express the problem globally (in terms of the cohomology of a blown-up twistor space), calculate the holomorphic Euler characteristic of this blown-up space, and then use some vanishing theorems to isolate the first cohomology term.     

Integrability in String/Field Theories and Hamiltonian Flows in the Space of Physical Systems

Integrability in string/field theories is known to emerge when considering dynamics in the moduli space of physical theories. This implies that one must study the dynamics with respect to unusual time variables such as coupling constants or other quantities parameterizing the configuration space of physical theories. The dynamics given by variations of coupling constants can be considered as a canonical transformation or, infinitesimally, a Hamiltonian flow in the space of physical systems. We briefly consider an example of integrable mechanical systems. Then any function T generates a one-parameter family of integrable systems in the vicinity of a single system. For an integrable system with several coupling constants, the corresponding Hamiltonians T_i satisfy the Whitham equations and, after quantization (of the original system), become operators satisfying the zero-curvature condition in the coupling-constant space.     

An efficient and simple refined theory for buckling analysis of functionally graded plates

In this paper, an efficient and simple refined theory is presented for buckling analysis of functionally graded plates. The theory, which has strong similarity with classical plate theory in many aspects, accounts for a quadratic variation of the transverse shear strains across the thickness and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factors. The mechanical properties of functionally graded material are assumed to vary according to a power law distribution of the volume fraction of the constituents. Governing equations are derived from the principle of minimum total potential energy. The closed-form solutions of rectangular plates are obtained. Comparison studies are performed to verify the validity of present results. The effects of loading conditions and variations of power of functionally graded material, modulus ratio, aspect ratio, and thickness ratio on the critical buckling load of functionally graded plates are investigated and discussed.     

Quintessence scalar field in the relativistic theory of gravity

We propose a variant of the quintessence theory in order to obtain an accelerated expansion of the Friedmann universe in the framework of the relativistic theory of gravity. The scalar field of dark energy creates the substance of quintessence. We show that the function V(Φ) that factors the Lagrangian of the scalar field Φ does not influence the evolution of the universe. We find some relations that allow finding the explicit time-dependence of Φ if only the function V(Φ) is chosen. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 3, pp. 551–560, September, 2007.