Monopole solutions to the Bogomolny equation as three-dimensional generalizations of the Kronecker series

The Dirac monopole on a three-dimensional torus is considered as a solution to the Bogomolny equation with non-trivial boundary conditions. The analytical continuation of the obtained solution is shown to be a three-dimensional generalization of the Kronecker series. It satisfies the corresponding functional equation and is invariant under modular transformations.Comment: 13 pages, 1 figur

BPS States in Omega Background and Integrability

We reconsider string and domain wall central charges in N=2 supersymmetric gauge theories in four dimensions in presence of the Omega background in the Nekrasov-Shatashvili (NS) limit. Existence of these charges entails presence of the corresponding topological defects in the theory - vortices and domain walls. In spirit of the 4d/2d duality we discuss the worldsheet low energy effective theory living on the BPS vortex in N=2 Supersymmetric Quantum Chromodynamics (SQCD). We discuss some aspects of the brane realization of the dualities between various quantum integrable models. A chain of such dualities enables us to check the AGT correspondence in the NS limit.Comment: 48 pages, 10 figures, minor changes, references added, typos correcte

Bootstrapping the superconformal index with surface defects

The analytic properties of the N = 2 superconformal index are given a physical interpretation in terms of certain BPS surface defects, which arise as the IR limit of supersymmetric vortices. The residue of the index at a pole in flavor fugacity is interpreted as the index of a superconformal field theory without this flavor symmetry, but endowed with an additional surface defect. The residue can be efficiently extracted by acting on the index with a difference operator of Ruijsenaars-Schneider type. By imposing the associativity constraints of S-duality, we are then able to evaluate the index of all generalized quiver theories of type A, for generic values of the three superconformal fugacities, with or without surface defects.Comment: 60 pages, 7 figure

ДИНАМИКА КАЧЕСТВА ЖИЗНИ ПАЦИЕНТОВ ПРИ ОПТИМИЗАЦИИ ИМПЛАНТАЦИОННОГО ПРОТЕЗИРОВАНИЯ И ОТНОШЕНИЕ ИХ К РЕЗУЛЬТАТАМ СТОМАТОЛОГИЧЕСКОГО ОРТОПЕДИЧЕСКОГО ЛЕЧЕНИЯ (СОЦИОЛОГИЧЕСКОЕ ИССЛЕДОВАНИЕ)

The life quality estimation of dental patients, especially with total adentia, before and after implant treatment is highly topical. A direct or immediate implant prosthodontics contributes to prompt restoration of impaired aesthetic and functional standards while urgently converting patients from a disability level to a high life quality category. However, mistakes and complications occurring in this treatment stage often result in patients’ discomfort and worsen their physical and psycho-emotional state. All these are not conductive to securely provided favourable results of dental implant prosthetics, and thus require further improvement of the clinical and conceptual approaches aimed at further optimization of the above specialized medical care. The authors succeeded in improving efficacy of immediate implant prosthodontics with extended orthopaedic constructions by means of optimizing the diagnostic and therapeutic resources, as well as the hygiene protocol.Оценка качества жизни стоматологических больных, особенно с полной потерей зубов, до и после имплантационного лечения является весьма актуальной. Непосредственное, или немедленное, имплантационное протезирование способствует скорейшему восстановлению нарушенных эстетических и функциональных норм, экстренно переводя пациентов с уровня инвалидизации до разряда высокого качества жизни. Однако ошибки и осложнения, возникающие на данном этапе лечения, зачастую вызывают дискомфорт у пациентов и ухудшают их физическое и психоэмоциональное состояние. Все это не способствует надежно гарантированным благоприятным исходам имплантационного протезирования и требует дальнейшего совершенствования клинических концептуальных подходов, направленных на дальнейшее совершенствование указанной специализированной медицинской помощи. Нам удалось повысить эффективность немедленного имплантационного протезирования протяженными ортопедическими конструкциями путем оптимизации диагностического, терапевтического ресурсов и гигиенического протокола

On integrable structure and geometric transition in supersymmetric gauge theories

We generalize the exact field theoretic correspondence proposed in [1] and embed it into the context of refined topological string. The correspondence originally proposed from the common integrable structures in different field theories can be recast as a special limit of the refined geometric transition relating open and closed topological string partition functions. We realize the simplest examples of the correspondence explicitly in terms of open-closed geometric transition

The stringy instanton partition function

We perform an exact computation of the gauged linear sigma model associated to a D1-D5 brane system on a resolved A 1 singularity. This is accomplished via supersymmetric localization on the blown-up two-sphere. We show that in the blow-down limit the partition function reduces to the Nekrasov partition function evaluating the equivariant volume of the instanton moduli space. For finite radius we obtain a tower of world-sheet instanton corrections, that we identify with the equivariant Gromov-Witten invariants of the ADHM moduli space. We show that these corrections can be encoded in a deformation of the Seiberg-Witten prepotential. From the mathematical viewpoint, the D1-D5 system under study displays a twofold nature: the D1-branes viewpoint captures the equivariant quantum cohomology of the ADHM instanton moduli space in the Givental formalism, and the D5-branes viewpoint is related to higher rank equivariant Donaldson-Thomas invariants