Categorified canonical bases and framed BPS states

Dylan G. L. Allegretti ^[1]
1. [1] Mathematical Sciences Research Institute, USA
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 25, Nº. 5, 2019
Idioma: inglés
DOI: 10.1007/s00029-019-0518-3
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Resumen
- We consider a cluster variety associated to a triangulated surface without punctures. The algebra of regular functions on this cluster variety possesses a canonical vector space basis parametrized by certain measured laminations on the surface. To each lamination, we associate a graded vector space, and we prove that the graded dimension of this vector space gives the expansion in cluster coordinates of the corresponding basis element. We discuss the relation to framed BPS states in N=2 field theories of class S.