Seiberg-Witten theory and random partitions
Nikita Nekrasov,Andrei Okounkov +1 more
- Vol. 244, pp 525-596
TLDR
In this paper, the authors investigated various representations for this partition function: a statistical sum over random partitions, a partition function of the ensemble of random curves, and a free fermion correlator.Abstract:
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 Ω-background can be calculated explicitly. We investigate various representations for this partition function: a statistical sum over random partitions, a partition function of the ensemble of random curves, and a free fermion correlator.read more
Citations
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Liouville Correlation Functions from Four-dimensional Gauge Theories
TL;DR: In this paper, the authors conjecture an expression for the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures as the Nekrasov partition function of a certain class of SCFTs recently defined by one of the authors.
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Localization of Gauge Theory on a Four-Sphere and Supersymmetric Wilson Loops
TL;DR: In this article, the authors proved conjecture due to Erickson-Semenoff-Zarembo and Drukker-Gross which relates supersymmetric circular Wilson loop operators with a Gaussian matrix model.
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Quantization of Integrable Systems and Four Dimensional Gauge Theories
TL;DR: In this paper, the authors studied four dimensional N=2 supersymmetric gauge theory in the Omega-background with the two dimensional N = 2 super-Poincare invariance and explained how this gauge theory provided the quantization of the classical integrable system underlying the moduli space of vacua of the ordinary four-dimensional N =2 theory, and showed the thermodynamic-Betheansatz like formulae for these functions and for the spectra of commuting Hamiltonians following the direct computation in gauge theory.
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A(N-1) conformal Toda field theory correlation functions from conformal N = 2 SU(N) quiver gauge theories
TL;DR: In this paper, a relation between correlation functions in the 2d A(N-1) conformal Toda theories and the Nekrasov instanton partition functions in certain conformal N = 2 SU(N) 4d quiver theories was proposed.
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Topological Strings and Integrable Hierarchies
TL;DR: In this paper, the authors consider the topological B-model on local Calabi-Yau geometries and show how one can solve for the amplitudes by using W-algebra symmetries which encodes the symmets of holomorphic diffeomorphisms of the Calabi Yau.
References
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String theory and noncommutative geometry
Nathan Seiberg,Edward Witten +1 more
TL;DR: In this article, a non-zero B-field is introduced for string theory and the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a noncommutative space, and the corrections away from this limit are discussed.
Journal ArticleDOI
Topological quantum field theory
TL;DR: A twisted version of four dimensional supersymmetric gauge theory is formulated in this paper, which refines a nonrelativistic treatment by Atiyah and appears to underlie many recent developments in topology of low dimensional manifolds; the Donaldson polynomial invariants of four manifolds and the Floer groups of three manifolds appear naturally.
Journal ArticleDOI
Pseudoparticle Solutions of the Yang-Mills Equations
TL;DR: In this article, the authors find regular solutions of the four dimensional euclidean Yang-Mills equations and show that these solutions minimize locally the action integrals, which is finite in this case.
Book
Gauge fields and strings
TL;DR: In this article, the authors synthesize the most promising approaches and ideals in field theory today, including statistical mechanics, quantum field theory and their interrelation, continuous global symmetry, non-Abelian gauge fields, instantons and the quantam theory of loops, and quantum strings and random surfaces.
Journal ArticleDOI
Current Algebra and Wess-Zumino Model in Two-Dimensions
TL;DR: In this article, the anomalous dimensions of the Wess-Zumino fields are found exactly, and the multipoint correlation functions are shown to satisfy linear differential equations, in particular, Witten's non-abelean bosonisation rules are proven.