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Operator algebra
About: Operator algebra is a research topic. Over the lifetime, 5783 publications have been published within this topic receiving 165303 citations.
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TL;DR: In this paper, the method of factorization of operators, which has been used to derive the Miura transformation of the KdV equation, is extended to some third-order scattering operators, and transformations between several fifth-order nonlinear evolution equations are derived.
Abstract: The method of factorization of operators, which has been used to derive the Miura transformation of the KdV equation, is here extended to some third‐order scattering operators, and transformations between several fifth‐order nonlinear evolution equations are derived. Further applications are discussed.
123 citations
TL;DR: In this paper, an effective algorithm to generate integrable systems is given, and many new integrably equations are derived in a systematic way, as well as an effective method to derive integrability equations.
Abstract: In this paper, an effective algorithm to generate integrable systems is given. As a result, many new integrable equations are derived in a systematic way.
123 citations
TL;DR: In this article, the authors use supersymmetric localization to calculate correlation functions of half-BPS local operators in 3D N=4 superconformal field theories whose Lagrangian descriptions consist of vectormultiplets coupled to hypermultiplets.
Abstract: We use supersymmetric localization to calculate correlation functions of half-BPS local operators in 3d N=4 superconformal field theories whose Lagrangian descriptions consist of vectormultiplets coupled to hypermultiplets. The operators we primarily study are certain twisted linear combinations of Higgs branch operators that can be inserted anywhere along a given line. These operators are constructed from the hypermultiplet scalars. They form a one-dimensional non-commutative operator algebra with topological correlation functions. The 2- and 3-point functions of Higgs branch operators in the full 3d N=4 theory can be simply inferred from the 1d topological algebra. After conformally mapping the 3d superconformal field theory from flat space to a round three-sphere, we preform supersymmetric localization using a supercharge that does not belong to any 3d N=2 subalgebra of the N=4 algebra. The result is a simple model that can be used to calculate correlation functions in the 1d topological algebra mentioned above. This model is a 1d Gaussian theory coupled to a matrix model, and it can be viewed as a gauge-fixed version of a topological gauged quantum mechanics. Our results generalize to non-conformal theories on S^3 that contain real mass and Fayet-Iliopolous parameters. We also provide partial results in the 1d topological algebra associated with the Coulomb branch, where we calculate correlation functions of local operators built from the vectormultiplet scalars.
122 citations
TL;DR: In this paper, the basic concepts of non-commutative probability theory are reviewed and applied to the large-N limit of matrix models, in terms of which large- N theories can be written.
122 citations
TL;DR: In this paper, a field-theoretical approach to the determination of the background target space fields corresponding to general G/H coset conformal theories described by gauged WZW models is presented.
122 citations