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Seiberg-Witten prepotential from instanton counting
Direct evaluation of the Seiberg-Witten prepotential is accomplished following the localization programme suggested in [1]. Our results agree with all low-instanton calculations available in the…
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Seiberg-Witten theory and random partitions
We study \( \mathcal{N} = 2 \) supersymmetric four-dimensional gauge theories, in a certain 525-02 = 2 supergravity background, called theΩ-background. The partition function of the theory in the…
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Quantization of Integrable Systems and Four Dimensional Gauge Theories
We study four dimensional N=2 supersymmetric gauge theory in the Omega-background with the two dimensional N=2 super-Poincare invariance. We explain how this gauge theory provides the quantization of…
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Instantons on Noncommutative ℝ4, and (2,0) Superconformal Six Dimensional Theory
Abstract:We show that the resolution of moduli space of ideal instantons parameterizes the instantons on noncommutative ℝ4. This moduli space appears to be the Higgs branch of the theory of…
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Gromov–Witten theory and Donaldson–Thomas theory, I
We conjecture an equivalence between the Gromov–Witten theory of 3-folds and the holomorphic Chern–Simons theory of Donaldson and Thomas. For Calabi–Yau 3-folds, the equivalence is defined by the…
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On conformal field theories in four dimensions
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D-Particle Bound States and Generalized Instantons
Abstract:We compute the principal contribution to the index in the supersymmetric quantum mechanical systems which are obtained by reduction to 0 + 1 dimensions of , D= 4,6,10 super-Yang–Mills…
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Noncommutative field theory
We review the generalization of field theory to space-time with noncommuting coordinates, starting with the basics and covering most of the active directions of research. Such theories are now known…
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BPS/CFT correspondence: non-perturbative Dyson-Schwinger equations and qq-characters
A bstractWe study symmetries of quantum field theories involving topologically distinct sectors of the field space. To exhibit these symmetries we define special gauge invariant observables, which we…
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Quantum foam and topological strings
We find an interpretation of the recent connection found between topological strings on Calabi-Yau threefolds and crystal melting: Summing over statistical mechanical configuration of melting crystal…
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