Alex Vainshtein

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We reexamine the issue of the soliton mass in two-dimensional models with N = 1 supersymmetry. The superalgebra has a central extension, and at the classical level the soliton solution preserves 1/2 of supersymmetry which is equivalent to BPS saturation. We prove that the property of BPS saturation, i.e. the equality of the soliton mass to the central(More)
In the present paper we apply the theory of skew-symmetric vanishing lattices developed around 15 years ago by B. Wajnryb, S. Chmutov, and W. Janssen for the necessities of the singularity theory to the enumeration of connected components in the intersection of two open opposite Schubert cells in the space of complete real ags. Let us brieey recall the main(More)
We derive the lepton spectrum in semileptonic beauty decays from a nonperturbative treatment of QCD; it is based on an expansion in 1/m Q with m Q being the heavy flavour quark mass. The leading corrections arising on the 1/m Q level are completely expressed in terms of the difference in the mass of the heavy hadron and the quark. Nontrivial effects appear(More)
In this paper we reduce the problem concerning the number of connected components in the intersection of two real opposite open Schubert cells in SL n (R)=B to a purely combinatorial question in the space of upper triangular matrices with F 2-valued entries. The crucial step of the reduction uses the parametrization of the space of real unipotent totally(More)
We study the distribution of the number of permutations with a given periodic up-down sequence w.r.t. the last entry, find exponential generating functions and prove asymptotic formulas for this distribution. Let σ = (σ 1 ,. .. , σ n) be a permutation of length n. We associate with σ its up-down sequence (sometimes called the shape of σ, or the signature of(More)
In the last few years considerable progress has been achieved in our understanding of the decays of heavy flavour hadrons. One can now calculate inclusive transition rates in QCD proper through an expansion in inverse powers of the heavy flavour quark mass without recourse to phenomenological assumptions. The non-perturbative contributions are treated(More)
We discuss the central charge in supersymmetric N = 2 sigma models in two dimensions. The target space is a symmetric Kähler manifold; CP(N −1) is an example. The U(1) isometries allow one to introduce twisted masses in the model. At the classical level the central charge contains Noether charges of the U(1) isometries and a topological charge which is an(More)