Toric Mutations in the dP$_2$ Quiver and Subgraphs of the dP$_2$ Brane Tiling | Zendy

Yibo Gao | Zendy; Zhaoqi Li | Zendy; Thuy-Duong Vuong | Zendy; Lisa Yang | Zendy

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Toric Mutations in the dP$_2$ Quiver and Subgraphs of the dP$_2$ Brane Tiling

Author(s) -

Yibo Gao,

Zhaoqi Li,

Thuy-Duong Vuong,

Lisa Yang

Publication year - 2019

Publication title -

the electronic journal of combinatorics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.703

H-Index - 52

eISSN - 1097-1440

pISSN - 1077-8926

DOI - 10.37236/6825

Subject(s) - quiver , mathematics , combinatorics , cluster algebra , bipartite graph , laurent polynomial , brane , discrete mathematics , pure mathematics , physics , graph , mathematical physics , quantum , quantum mechanics

Brane tilings are infinite, bipartite, periodic, planar graphs that are dual to quivers. In this paper, we examine the del Pezzo 2 (dP$_2$) quiver and its brane tiling, which arise from the physics literature, in terms of toric mutations on its corresponding cluster. Specifically, we give explicit formulas for all cluster variables generated by toric mutation sequences. Moreover, for each such variable, we associate a subgraph of the dP$_2$ brane tiling to it such that its weight matches the variable.

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