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P. B. Medvedev

Publications and source records attributed to P. B. Medvedev.

At least 19 recordsLinked to original sources
arXiv2009

Pure Gauge Configurations and Solutions to Fermionic Superstring Field Theories Equations of Motion

Recent results on solutions to the equation of motion of the cubic fermionic string field theory and an equivalence of non-polynomial and cubic string field theories are discussed. To have a possibility to deal with both GSO(+) and GSO(-) sectors in the uniform way a matrix formulation for the NS fermionic SFT is used. In constructions of analytical solutions to open string field theories truncated pure gauge configurations parameterized by wedge states play an essential role. The matrix form of this parametrization for the NS fermionic SFT is presented. Using the cubic open superstring field theory as an example we demonstrate explicitly that for the large parameter of the perturbation expansion these truncated pure gauge configurations give divergent contributions to the equation of motion on the subspace of the wedge states. The perturbation expansion is cured by adding extra terms that are nothing but the terms necessary for the equation of motion contracted with the solution itself to be satisfied.

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arXiv2009

Pure Gauge Configurations and Tachyon Solutions to String Field Theories Equations of Motion

In constructions of analytical solutions to open string field theories pure gauge configurations parameterized by wedge states play an essential role. These pure gauge configurations are constructed as perturbation expansions and to guaranty that these configurations are asymptotical solutions to equations of motions one needs to study convergence of the perturbation expansions. We demonstrate that for the large parameter of the perturbation expansion these pure gauge truncated configurations give divergent contributions to the equation of motion on the subspace of the wedge states. We perform this demonstration numerically for the pure gauge configurations related to tachyon solutions for the bosonic and the NS fermionic SFT. By the numerical calculations we also show that the perturbation expansions are cured by adding extra terms. These terms are nothing but the terms necessary to make valued the Sen conjectures.

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arXiv2008

Descent Relations in Cubic Superstring Field Theory

The descent relations between string field theory (SFT) vertices are characteristic relations of the operator formulation of SFT and they provide self-consistency of this theory. The descent relations and in the NS fermionic string field theory in the kappa and discrete bases are established. Different regularizations and schemes of calculations are considered and relations between them are discussed.

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arXiv2006

Descent Relations and Oscillator Level Truncation Method

We reexamine the oscillator level truncation method in the bosonic String Field Theory (SFT) by calculation the descent relation =Z_3<V_2|. For the ghost sector we use the fermionic vertices in the standard oscillator basis. We propose two new schemes for calculations. In the first one we assume that the insertion satisfies the overlap equation for the vertices and in the second one we use the direct calculations. In both schemes we get the correct structures of the exponent and pre-exponent of the vertex <V_2|, but we find out different normalization factors Z_3.

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arXiv2002

NS Matter Sliver

Using algebraic methods the Neveu-Schwarz fermionic matter sliver is constructed. Inspirited by the wedge algebra two equations for the sliver, linear and quadratic, are considered. It is shown that both equations give the same nontrivial answer. The sliver is considered also using CFT methods where it is defined as the limit of the wedge states in the NS sector of the superstring.

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arXiv2002

Noncommutative Field Theories and (Super)String Field Theories

In this lecture notes we explain and discuss some ideas concerning noncommutative geometry in general, as well as noncommutative field theories and string field theories. We consider noncommutative quantum field theories emphasizing an issue of their renormalizability and the UV/IR mixing. Sen's conjectures on open string tachyon condensation and their application to the D-brane physics have led to wide investigations of the covariant string field theory proposed by Witten about 15 years ago. We review main ingredients of cubic (super)string field theories using various formulations: functional, operator, conformal and the half string formalisms. The main technical tools that are used to study conjectured D-brane decay into closed string vacuum through the tachyon condensation are presented. We describe also methods which are used to study the cubic open string field theory around the tachyon vacuum: construction of the sliver state, ``comma'' and matrix representations of vertices.

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arXiv2001

Gauge Invariance and Tachyon Condensation in Cubic Superstring Field Theory

The gauge invariance of cubic open superstring field theory is considered in a framework of level truncation, and applications to the tachyon condensation problem are discussed. As it is known, in the bosonic case the Feynman-Siegel gauge is not universal within the level truncation method. We explore another gauge that is more suitable for calculation of the tachyon potential for fermionic string at level (2,6). We show that this new gauge has no restrictions on the region of its validity at least at this level.

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arXiv2001

Tachyon condensation in cubic superstring field theory

It has been conjectured that at the stationary point of the tachyon potential for the non-BPS D-brane or brane-anti-D-brane pair, the negative energy density cancels the brane tension. We study this conjecture using a cubic superstring field theory with insertion of a double-step inverse picture changing operator. We compute the tachyon potential at levels (1/2,1) and (2,6). In the first case we obtain that the value of the potential at the minimum is 97.5% of the non BPS D-brane tension. Using a special gauge in the second case we get 105.8% of the tension.

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arXiv1999

On Stable Sector in Supermembrane Matrix Model

We study the spectrum of SU(2) x SO(2) matrix supersymmetric quantum mechanics. We use angular coordinates that allow us to find an explicit solution of the Gauss law constraints and single out the quantum number n (the Lorentz angular momentum). Energy levels are four-fold degenerate with respect to n and are labeled by n_q, the largest n in a quartet. The Schrödinger equation is reduced to two different systems of two-dimensional partial differential equations. The choice of a system is governed by n_q. We present the asymptotic solutions for the systems deriving thereby the asymptotic formula for the spectrum. Odd n_q are forbidden, for even n_q the spectrum has a continuous part as well as a discrete one, meanwhile for half-integer n_q the spectrum is purely discrete. Taking half-integer n_q one can cure the model from instability caused by the presence of continuous spectrum.

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arXiv1998

Chaos-Order Transition in Matrix Theory

Classical dynamics in SU(2) Matrix theory is investigated. A classical chaos-order transition is found. For the angular momentum small enough (even for small coupling constant) the system exhibits a chaotic behavior, for angular momentum large enough the system is regular.

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arXiv1997

Chaos in M(atrix) Theory

We consider the classical and quantum dynamics in M(atrix) theory. Using a simple ansatz we show that a classical trajectory exhibits a chaotic motion. We argue that the holographic feature of M(atrix) theory is related with the repulsive feature of energy eigenvalues in quantum chaotic system. Chaotic dynamics in N=2 supersymmetric Yang-Mills theory is also discussed. We demonstrate that after the separation of "slow" and "fast" modes there is a singular contribution from the "slow" modes to the Hamiltonian of the "fast" modes.

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arXiv1995

$N$-point amplitudes for d=2 c=1 Discrete States from String Field Theory

Starting from string field theory for 2d gravity coupled to c=1 matter we analyze N-point off-shell tree amplitudes of discrete states. The amplitudes exhibit the pole structure and we use the oscillator representation to extract the residues. The residues are generated by a simple effective action. We show that the effective action can be directly deduced from a string field action in a special transversal-like gauge.

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arXiv1994

On Poisson-Lie structure on the external algebra of the classical Lie groups

The general expression for the bicovariant bracket for odd generators of the external algebra on a Poisson-Lie group is given. It is shown that the graded Poisson-Lie structures derived before for $GL(N)$ and $SL(N)$ are the special cases of this bracket. The formula is the universal one and can be applied to the case of any matrix Lie group.

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arXiv1994

Quantization of the external algebra on a Poisson-Lie group

We show that the external algebra $\cal M$ on $GL(N)$ can be equipped with the graded Poisson brackets compatible with the group action. We prove that there are only two graded Poisson-Lie structures (brackets) on $\cal M$ and we obtain their explicit description. We realize that just these two structures appear as the quasiclassical limit of the bicovariant differential calculi on the quantum linear group $GL_q (N)$.

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