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Home > Journal of High Energy Physics (Springer/SISSA) > Plane partition realization of (web of) W $$ \mathcal{W} $$ -algebra minimal models |

Harada, Koichi (0000 0001 2151 536X, Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan) ; Matsuo, Yutaka (0000 0001 2151 536X, Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan)

10 February 2019

**Abstract: **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, N $$ \mathcal{N} $$ = 2 superconformal algebra, we demonstrate that the improved rule precisely reproduces the known character of the minimal models.

**Published in: ****JHEP 1902 (2019) 050**
**Published by: **Springer/SISSA

**DOI: **10.1007/JHEP02(2019)050

**arXiv: **1810.08512

**License: **CC-BY-4.0