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arXiv · 1810.08512

Plane Partition Realization of (Web of) W-algebra Minimal Models

Koichi Harada·Yutaka Matsuo
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Abstract

Recently, Gaiotto and Rapcak (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. Prochazka and Rapcak, 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, N=2 superconformal algebra, we demonstrate that the improved rule precisely reproduces the known character of the minimal models.

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Koichi Harada, Yutaka Matsuo. 2018-10-19. Plane Partition Realization of (Web of) W-algebra Minimal Models. https://doi.org/10.1007/jhep02(2019)050

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