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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 article, the authors consider high spin operators and give a general argument for the logarithmic scaling of their anomalous dimensions which is based on the symmetries of the problem.
Abstract: We consider high spin operators. We give a general argument for the logarithmic scaling of their anomalous dimensions which is based on the symmetries of the problem. By an analytic continuation we can also see the origin of the double logarithmic divergence in the Sudakov factor. We show that the cusp anomalous dimension is the energy density for a flux configuration of the gauge theory on AdS3 × S1. We then focus on operators in = 4 super Yang Mills which carry large spin and SO(6) charge and show that in a particular limit their properties are described in terms of a bosonic O(6) sigma model. This can be used to make certain all loop computations in the string theory.

395 citations

Journal ArticleDOI
TL;DR: In this paper, the integrability of the system of PDE for dependence on coupling parameters of the (tree-level) primary partition function in massive topological field theories, being imposed by the associativity of the perturbed primary chiral algebra, is proved.

391 citations

Journal ArticleDOI
TL;DR: In this paper, the authors give new examples of non-commutative manifolds that are less standard than the NC-torus or Moyal deformations of ℝn.
Abstract: We give new examples of noncommutative manifolds that are less standard than the NC-torus or Moyal deformations of ℝn. They arise naturally from basic considerations of noncommutative differential topology and have non-trivial global features.

381 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that there is a natural structure of a Batalin-Vilkovisky algebra on the cohomology of a topological conformal field theory in two dimensions.
Abstract: By a Batalin-Vilkovisky algebra, we mean a graded commutative algebraA, together with an operator Δ:A⊙→A⊙+1 such that Δ2 = 0, and [Δ,a]−Δa is a graded derivation ofA for alla∈A. In this article, we show that there is a natural structure of a Batalin-Vilkovisky algebra on the cohomology of a topological conformal field theory in two dimensions. We make use of a technique from algebraic topology: the theory of operads.

378 citations

Posted Content
TL;DR: In this paper, the relationship between the Verlindealgebra of the group U(k) at level N k and the quantum cohom ology of the Grassm annian ofcom plex k planes in N space is explained.
Abstract: Thearticleisdevoted toaquantumeld theoryexplanation oftherelationship between theVerlindealgebra ofthegroup U(k)atlevel N k and the\quantum " cohom ology oftheGrassm annian ofcom plex k planesin N space.In x2,Iexplain therelation between theVerlindealgebra and thegauged W ZW m odelof G=G;in x3,Idescribe the quantum cohom ology and itsorigin in a quantumeld theory; and in x4,Ipresenta path integralargum entform apping between them .

377 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202337
202277
2021125
2020141
2019173
2018169