Related papers: Operator Mapping between RNS and Extended Pure Spi…
The character of holomorphic functions on the space of pure spinors in ten, eleven and twelve dimensions is calculated. From this character formula, we derive in a manifestly covariant way various central charges which appear in the pure…
Brane-like states are defined by physical vertex operators in NSR superstring theory, existing at nonzero pictures only. These states exist both in open and closed string theories, in the NS and NS-NS sectors respectively. In this paper we…
The suggested operator manifold formalism enables to develop an approach to the unification of the geometry and the field theory. We also elaborate the formalism of operator multimanifold yielding the multiworld geometry involving the…
Using the pure spinor formalism, we compute the tree-level correlation functions for three strings, one closed and two open, in N=1 D=10 superspace. Expanding the superfields in components, the respective terms of the effective action for…
A dynamical map is a map which takes one density operator to another. Such a map can be written in an operator-sum representation (OSR) using a spectral decomposition. The method of the construction applies to more general maps which need…
This article contains a characterization of operator systems $\cS$ with the property that every positive map $\phi:\cS \rightarrow M_n$ is decomposable, as well as an alternate and a more direct proof of a characterization of decomposable…
The lambda deformation of the pure spinor formalism of the superstring in the $AdS_{5}\times S^{5}$ background is introduced. It is shown that the deformation preserves the integrability as well as the one-loop conformal invariance of its…
We present a prescription for computing tree-level scattering amplitudes in 10D super-Yang-Mills (SYM) theory using the pure spinor worldline formalism. The pure spinor formalism has proven to be a powerful framework for studying…
We compactify the pure spinor formalism on a K3 surface. The pure spinor splits into a six-dimensional pure spinor, a projective superspace harmonic, and 6 non-covariant variables. A homological algebra argument reduces the calculation of…
In this paper the pure spinor formalism is used to obtain a compact expression for the superstring N-point disk amplitude. The color ordered string amplitude is given by a sum over (N-3)! super Yang-Mills subamplitudes multiplied by…
We use the non-minimal pure spinor formalism to compute in a super-Poincare covariant manner the four-point massless one and two-loop open superstring amplitudes, and the gauge anomaly of the six-point one-loop amplitude. All of these…
In the recent years, a lot of attention has been paid to the development of solid foundations for the composition and inversion of schema mappings. In this paper, we review the proposals for the semantics of these crucial operators. For…
We exploit the key concepts of the augmented version of superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism to derive the superspace (SUSP) dual unitary operator (and its Hermitian conjugate) and demonstrate their utility in…
In the first part of the talk I report on surprising relations between higher spin (HS) theory and nonlinear realizations of the supergroup OSp(1|8), a minimal superconformal extension of N=1, 4D supersymmetry with tensorial charges. The…
I report on the development of a novel statistical mechanical formalism for the analysis of random graphs with many short loops, and processes on such graphs. The graphs are defined via maximum entropy ensembles, in which both the degrees…
We compute the massless five-point amplitude of open superstrings using the non-minimal pure spinor formalism and obtain a simple kinematic factor in pure spinor superspace, which can be viewed as the natural extension of the kinematic…
We construct an index for BPS operators supported on a ray in five dimensional superconformal field theories with exceptional global symmetries. We compute the $E_n$ representations (for $n=2,\dots,7$) of operators of low spin, thus…
We develop a supersymmetric representation of spin operators which unifies the Schwinger and Abrikosov representations of SU(N) spin operators, allowing a second-quantized treatment of representations of the SU(N) group with both symmetric…
The article consists of the Russian and English variants of Ph.D. Thesis in which the answers is given on the following questions: 1. how to construct the spinor formalism for n=6; 2. how to construct the spinor formalism for n=8; 3. how to…
We establish the equivalence between two formulations of superstring perturbation theory, one based on integration over the supermoduli space of super Riemann surfaces (SRS), the other based on integration over the bosonic moduli space with…