?
Instantons in sigma model and tau functions
arXiv:1611.02248
,
2016.
Antonov E., Orlov A. Y.
We show that a number of multiple integrals may viewed as tau functions of various integrable hierarchies.
The instanton contributions in the two-dimensional O(3) sigma model is an example of such an approach.
Priority areas:
mathematics
Language:
English
Keywords: instantons
Publication based on the results of:
Tikhomirov A. S., Markushevich D., Trautmann G., Central European Journal of Mathematics 2012 Vol. 19 No. 4 P. 1331-1355
We announce some results on compactifying moduli spaces of rank 2 vector bundles on surfaces by spaces of vector vector bundles on trees of surfaces. This is thought as an algebraic counterpart of the so-called bubbling of vector bundled connections an in differential geometry. The new moduli spaces are algebraic spaces arising as quotients ...
Added: October 21, 2014
Kolokolov I., Lebedev V., Falkovich G. et al., Physical Review Letters 1997 Vol. 78 No. 8 P. 1452-1455
We consider the tails of probability density function (PDF) for the velocity that satisfies Burgers equation driven by a Gaussian large-scale force. The saddle-point approximation is employed in the path integral so that the calculation of the PDF tails boils down to finding the special field-force configuration (instanton) that realizes the extremum of probability. For ...
Added: March 6, 2017
Jardim M., Markushevich D., Tikhomirov A. S., Moscow Mathematical Journal 2018 Vol. 18 No. 1 P. 117-148
Abstract. Let I(n) denote the moduli space of rank 2 instanton bundles of charge n on P3 . It is known that I(n) is an irreducible, nonsingular and affine variety of dimension 8n − 3. Since every rank 2 instanton bundle on P3 is stable, we may regard I(n) as an open subset of the ...
Added: August 20, 2018
Kolokolov I., Lebedev V., Falkovich G. et al., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 1996 Vol. 54 No. 5 P. 4896
We describe the method for finding the non-Gaussian tails of the probability distribution function (PDF) for solutions of a stochastic differential equation, such as the convection equation for a passive scalar, the random driven Navier-Stokes equation, etc. The existence of such tails is generally regarded as a manifestation of the intermittency phenomenon. Our formalism is ...
Added: March 8, 2017
Jardim M., Markushevich D., Tikhomirov A. S., Annali di Matematica Pura ed Applicata 2017 Vol. 196 No. 4 P. 1573-1608
We describe new components of the Gieseker–Maruyama moduli scheme (Formula presented.) of semistable rank 2 sheaves E on (Formula presented.) with (Formula presented.), (Formula presented.) and (Formula presented.) whose generic point corresponds to nonlocally free sheaves. We show that such components grow in number as n grows, and discuss how they intersect the instanton component. ...
Added: February 18, 2017
Kolokolov I., Lebedev V., Falkovich G. et al., International Journal of Modern Physics B 1997 Vol. 11 No. 26/27 P. 3223-3245
We consider
the tails of probability density functions (PDF) for different characteristics
of velocity that satisfies Burgers equation driven by a large-scale force.
The saddle-point approximation is employed in the path integral
so that the calculation of the PDF tails
boils down to finding the special field-force configuration (instanton) that
realizes the extremum of probability. We calculate high moments of the ...
Added: March 6, 2017
Musaev E., Haupt A., Lechtenfeld O., Journal of High Energy Physics 2014 Vol. 2014 No. 11
Abstract: We consider (1+3)-dimensional domain wall solutions of heterotic supergravity on a six-dimensional warped nearly Kaehler manifold $X_6$ in the presence of gravitational and gauge instantons of tanh-kink type as constructed in [1]. We include first order alpha' corrections to the heterotic supergravity action, which imply a non-trivial Yang-Mills sector and Bianchi identity. We present ...
Added: December 8, 2014
Bruzzo U., Markushevich D., Tikhomirov A. S., European Journal of Mathematics 2016 Vol. 2 P. 73-86
We study the moduli space $I_{n,r}$In,r of rank-2r symplectic instanton vector bundles on $\mathbb{P}^3$ℙ3 with $r\ge 2$r⩾2 and second Chern class $n\ge r+1, n-r\equiv 1(\mathrm{mod} 2)$n⩾r+1,n−r≡1(mod2). We introduce the notion of tame symplectic instantons by excluding a kind of pathological monads and show that the locus $I_{n,r}^*$I∗n,r of tame symplectic instantons is irreducible and has the expected dimension equal to ...
Added: December 28, 2015
Tikhomirov A. S., Bruzzo U., Markushevich D., Mathematische Zeitschrift 2013 Vol. 275 No. 3-4 P. 1073-1093
We construct a compactification $M^{μss}$ of the Uhlenbeck–Donaldson type for the moduli space of slope stable framed bundles. This is a kind of a moduli space of slope semistable framed sheaves. We show that there exists a projective morphism $\gamma: M^{ss}\to M^{μss}$, where $M^{μss}$ is the moduli space of $S$-equivalence classes of Gieseker-semistable framed sheaves. ...
Added: October 20, 2014
Tikhomirov A. S., Markushevich D., Verbitsky M., Central European Journal of Mathematics 2012 Vol. 10 No. 4 P. 1185-1187
In this preface we give a short description of the current issue of the Central European Journal of Mathematics containing 22 papers which spin around the topics of the conference “Instantons in complex geometry”, held on March 14–18, 2011 in Moscow. The main goal of the conference was to bring together specialists in complex algebraic ...
Added: October 21, 2014
Karasev M., Novikova E., Vybornyi E., Mathematical notes 2017 Vol. 102 No. 5-6 P. 776-786
In the model of Penning trap with a geometric asymmetry we study a resonance regime which produces a hyperbolic type algebra of integrals of motion. The algebra has qubic (non-Lie) commutation relations with creation-anihilation structure. The anharmonic part of the trap potential determines a top-like Hamiltonian over this algebra. The symmetry breaking term generates a ...
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Belavin A. A., Bershtein M., Feigin B. L. et al., Communications in Mathematical Physics 2012 P. 1-33
The recently proposed relation between conformal field theories in two dimensions and supersymmetric gauge theories in four dimensions predicts the existence of the distinguished basis in the space of local fields in CFT. This basis has a number of remarkable properties: one of them is the complete factorization of the coefficients of the operator product ...
Added: February 7, 2013
191574970, Functional Analysis and Its Applications 2006 Vol. 40 No. 2 P. 81-90
It is well known that every module M over the algebra ℒ(X) of operators on a finite-dimensional space X can be represented as the tensor product of X by some vector space E, M ≅ = E ⊗ X. We generalize this assertion to the case of topological modules by proving that if X is a stereotype space with the stereotype approximation property, then for each stereotype module M over the ...
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Losev A. S., Slizovskiy S., JETP Letters 2010 Vol. 91 P. 620-624
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Ilyashenko Y., Яковенко С. Ю., М. : МЦНМО, 2013
Предлагаемая книга—первый том двухтомной монографии, посвящённой аналитической теории дифференциальных уравнений.
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Added: February 5, 2014
Kalyagin V.A., Koldanov A.P., Koldanov P.A. et al., Physica A: Statistical Mechanics and its Applications 2014 Vol. 413 No. 1 P. 59-70
A general approach to measure statistical uncertainty of different filtration techniques for market network analysis is proposed. Two measures of statistical uncertainty are introduced and discussed. One is based on conditional risk for multiple decision statistical procedures and another one is based on average fraction of errors. It is shown that for some important cases ...
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Maslov V., Теоретическая и математическая физика 2019 Т. 201 № 1 С. 65-83
We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint
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Pahomov F., Известия РАН. Серия математическая 2016 Т. 80 № 6 С. 173-216
Полимодальная логика доказуемости
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We study a family of nonautonomous generalized Liénard-type equations. We consider the equivalence problem via the generalized Sundman transformations between this family of equations and type-I Painlevé–Gambier equations. As a result, we find four criteria of equivalence, which give four integrable families of Liénard-type equations. We demonstrate that these criteria can be used to construct ...
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The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...
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Kolokolov I., Lebedev V., Sizov G. A., Journal of Experimental and Theoretical Physics 2011 Vol. 140 No. 2 P. 387-400
We analyze magnetic kinematic dynamo in a conducting fluid where the stationary shear flow is accompanied by relatively weak random velocity fluctuations. The diffusionless and diffusion regimes are described. The growth rates of the magnetic field moments are related to the statistical characteristics of the flow describing divergence of the Lagrangian trajectories. The magnetic field ...
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Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18
Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
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Vyalyi M., Дискретная математика 1991 Т. 3 № 3 С. 35-45
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