Group Theoretical Structure and Inverse Scattering Method for super-KdV Equation

Using the group-theoretical approach to the inverse scattering method the supersymmetric Korteweg-de Vries equation is obtained by application of the Drinfeld-Sokolov reduction to osp(1|2) loop superalgebra. The direct and inverse scattering problems are discussed for the corresponding Lax pair.Comment: LaTeX2e, 19 pages, Zapiski Nauchnih Seminarov POMI (Steklov Institute), vol. 291, 185-205, 2002 (in russian); Engl. transl. : Journal of Math. Sci., Kluwer, in pres

Quantum Inverse Scattering Method and (Super)Conformal Field Theory

In this paper we consider the possibility of application of the quantum inverse scattering method for studying the superconformal field theory and it's integrable perturbations. The classical limit of the considered constructions is based on $\hat{osp}(1|2)$ super-KdV hierarchy. The quantum counterpart of the monodromy matrix corresponding to the linear problem associated with the L-operator is introduced. Using the explicit form of the irreducible representations of $\hat{osp}_q(1|2)$, the ``fusion relations'' for the transfer-matrices (i.e. the traces of the monodromy matrices in different representations) are obtained.Comment: LaTeX2e, 15 pages, Theor. Math. Phys., 2005, in pres

Quantum K-theory of Quiver Varieties and Many-Body Systems

We define quantum equivariant K-theory of Nakajima quiver varieties. We discuss type A in detail as well as its connections with quantum XXZ spin chains and trigonometric Ruijsenaars-Schneider models. Finally we study a limit which produces a K-theoretic version of results of Givental and Kim, connecting quantum geometry of flag varieties and Toda lattice.Comment: v3: 33 pages, some clarifications and correction

Quantization of the N=2 Supersymmetric KdV Hierarchy

We continue the study of the quantization of supersymmetric integrable KdV hierarchies. We consider the N=2 KdV model based on the $sl^{(1)}(2|1)$ affine algebra but with a new algebraic construction for the L-operator, different from the standard Drinfeld-Sokolov reduction. We construct the quantum monodromy matrix satisfying a special version of the reflection equation and show that in the classical limit, this object gives the monodromy matrix of N=2 supersymmetric KdV system. We also show that at both the classical and the quantum levels, the trace of the monodromy matrix (transfer matrix) is invariant under two supersymmetry transformations and the zero mode of the associated U(1) current.Comment: LaTeX2e, 12 page

Integrable Structure of Superconformal Field Theory and Quantum super-KdV Theory

The integrable structure of the two dimensional superconformal field theory is considered. The classical counterpart of our constructions is based on the $\hat{osp}(1|2)$ super-KdV hierarchy. The quantum version of the monodromy matrix associated with the linear problem for the corresponding L-operator is introduced. Using the explicit form of the irreducible representations of $\hat{osp}_q(1|2)$, the so-called "fusion relations" for the transfer matrices considered in different representations of $\hat{osp}_q(1|2)$ are obtained. The possible integrable perturbations of the model (primary operators, commuting with integrals of motion) are classified and the relation with the supersymmetric $\hat{osp}(1|2)$ Toda field theory is discussed.Comment: LaTeX2e, elsart.cls, 11 pages, subm. to Physics Letters

Beta-gamma systems and the deformations of the BRST operator

We describe the relation between simple logarithmic CFTs associated with closed and open strings, and their "infinite metric" limits, corresponding to the beta-gamma systems. This relation is studied on the level of the BRST complex: we show that the consideration of metric as a perturbation leads to a certain deformation of the algebraic operations of the Lian-Zuckerman type on the vertex algebra, associated with the beta-gamma systems. The Maurer-Cartan equations corresponding to this deformed structure in the quasiclassical approximation lead to the nonlinear field equations. As an explicit example, we demonstrate, that using this construction, Yang-Mills equations can be derived. This gives rise to a nontrivial relation between the Courant-Dorfman algebroid and homotopy algebras emerging from the gauge theory. We also discuss possible algebraic approach to the study of beta-functions in sigma-models.Comment: LaTeX2e, 15 pages; minor revision, typos corrected, Journal of Physics A, in pres

Superconformal Field Theory and SUSY N=1 KdV Hierarchy I: Vertex Operators and Yang-Baxter Equation

The supersymmetry invariant integrable structure of two-dimensional superconformal field theory is considered. The classical limit of the corresponding infinite family of integrals of motion (IM) coincide with the family of IM of SUSY N=1 KdV hierarchy. The quantum version of the monodromy matrix, generating quantum IM, associated with the SUSY N=1 KdV is constructed via vertex operator representation of the quantum R-matrix. The possible applications to the perturbed superconformal models are discussed.Comment: LaTeX2e, elsart.cls, 11 pages, subm. to Physics Letters

Quantum Supersymmetric Toda-mKdV Hierarchies

In this paper we generalize the quantization procedure of Toda-mKdV hierarchies to the case of arbitrary affine (super)algebras. The quantum analogue of the monodromy matrix, related to the universal R-matrix with the lower Borel subalgebra represented by the corresponding vertex operators is introduced. The auxiliary L-operators satisfying RTT-relation are constructed and the quantum integrability condition is obtained. General approach is illustrated by means of two important examples.Comment: LaTeX2e, elsart.cls, 21 pages, Nuclear Physics B, 2005, in pres

Never-breastfed children face a higher risk of suboptimal cognition at 2 years of corrected age: A multinational cohort of very preterm children

In a cohort of children born very preterm (VPT), we investigated the association between breast milk feeding (BMF) initiation and its duration on cognitive development at 2 years of corrected age. Data were obtained from the Effective Perinatal Intensive Care in Europe population-based prospective cohort of children born <32 weeks of gestation, in 11 European countries, in 2011–2012. The study sample included 4323 children. Nonverbal cognitive ability was measured applying the Parental Report of Children's Abilities, except for France where the problem-solving domain of the Ages & Stages Questionnaire was used. Verbal cognition was based on the number of words the child could say. To determine the association between BMF (mother's own milk) and nonverbal and verbal cognition (outcome categorized as optimal and suboptimal), adjusted risk ratios (aRRs) were estimated fitting Poisson regression models, with inverse probability weights to account for nonresponse bias. Overall, 16% and 11% of the children presented suboptimal nonverbal and verbal cognition, respectively. Never BMF was associated with a significantly increased risk for suboptimal nonverbal (aRR = 1.29, 95% confidence interval [CI] = 1.09–1.53) and verbal (aRR = 1.45, 95% CI = 1.09–1.92) cognitive development compared with those ever breastfed, after adjustment for perinatal and sociodemographic characteristics. Compared with children breastfed 6 months or more, children with shorter BMF duration exhibited a statistically nonsignificant elevated aRR. VPT children fed with breast milk had both improved nonverbal and verbal cognitive development at 2 years in comparison with never breastfed, independently of perinatal and sociodemographic characteristics. This study encourages targeted interventions to promote BMF among these vulnerable children. © 2022 The Authors. Maternal & Child Nutrition published by John Wiley & Sons Ltd.The authors are grateful to the parents and infants enrolled in the EPICE cohort and acknowledge all members of the staff in the Departments of Obstetrics and Neonatology from the hospitals in the EPICE regions. The research received funding from the European Union's Seventh Framework Programme (FP7/2007‐2013) under grant agreement number 259882 and received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement number 633724. Additional funding is acknowledged from the following regions: France (French Institute of Public Health Research/Institute of Public Health and its partners the French Health Ministry, the National Institute of Health and Medical Research, the National Institute of Cancer and the National Solidarity Fund for Autonomy; grant ANR‐11‐EQPX‐0038 from the National Research Agency through the French Equipex Programme of Investments in the Future; and the PremUp Foundation); Germany (PRIMAL Consortium, German Ministry for Education and Research); Poland (2012–2015 allocation of funds for international projects from the Polish Ministry of Science and Higher Education); Sweden (Stockholm County Council [ALF‐project and Clinical Research Appointment] and by the Department of Neonatal Medicine, Karolinska University Hospital), and UK (funding for The Neonatal Survey from Neonatal Networks for East Midlands and Yorkshire and the Humber regions). This study received additional funding from PESSOA Programme (2017–2018)—Hubert Curien Programme, under the Transnational cooperation between Portugal (FCT) and France (CAMPUS FRANCE). This study was also funded by national funding from the Foundation for Science and Technology—FCT, under the Unidade de Investigação em Epidemiologia–Instituto de Saúde Pública da Universidade do Porto (EPIUnit) (UIDB/04750/2020); the PhD Grant SFRH/BD/111794/2015 (Carina Rodrigues) was cofunded by the FCT and the POCH/FSE Program