Journal of High Energy Physics

, 2019:50 | Cite as

Plane partition realization of (web of) \( \mathcal{W} \)-algebra minimal models

  • Koichi HaradaEmail author
  • Yutaka Matsuo
Open Access
Regular Article - Theoretical Physics


Recently, Gaiotto and Rapčák (GR) proposed a new family of the vertex operator algebra (VOA) as the symmetry appearing at an intersection of five-branes to which they refer as Y algebra. Procházka and Rapčák, then proposed to interpret Y algebra as a truncation of affine Yangian whose module is directly connected to plane partitions (PP). They also developed GR’s idea to generate a new VOA by connecting plane partitions through an infinite leg shared by them and referred it as the web of W-algebra (WoW). In this paper, we demonstrate that double truncation of PP gives the minimal models of such VOAs. For a single PP, it generates all the minimal model irreducible representations of W-algebra. We find that the rule connecting two PPs is more involved than those in the literature when the U(1) charge connecting two PPs is negative. For the simplest nontrivial WoW, \( \mathcal{N} \) = 2 superconformal algebra, we demonstrate that the improved rule precisely reproduces the known character of the minimal models.


Conformal and W Symmetry Conformal Field Theory Supersymmetric Gauge Theory 


Open Access

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of PhysicsThe University of TokyoTokyoJapan

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