\( \mathcal{W} \) -symmetry, topological vertex and affine Yangian

Open Access
Regular Article - Theoretical Physics

Abstract

We discuss the representation theory of the non-linear chiral algebra \( {\mathcal{W}}_{1+\infty } \) of Gaberdiel and Gopakumar and its connection to the Yangian of \( \widehat{\mathfrak{u}(1)} \) whose presentation was given by Tsymbaliuk. The characters of completely degenerate representations of \( {\mathcal{W}}_{1+\infty } \) are given by the topological vertex. The Yangian picture provides an infinite number of commuting charges which can be explicitly diagonalized in \( {\mathcal{W}}_{1+\infty } \) highest weight representations. Many properties that are difficult to study in the \( {\mathcal{W}}_{1+\infty } \) picture turn out to have a simple combinatorial interpretation, once translated to the Yangian picture.

Keywords

Conformal and W Symmetry Higher Spin Symmetry Field Theories in Lower Dimensions 

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Copyright information

© The Author(s) 2016

Authors and Affiliations

  1. 1.Arnold Sommerfeld Center for Theoretical PhysicsLudwig Maximilian University of MunichMünchenGermany
  2. 2.Institute of Physics AS CRPrague 8Czech Republic

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