Department of Mathematics, University of Texas at Austin, Austin, TX 78712
Proc Natl Acad Sci U S A. 2014 Jul 8;111(27):9717-24. doi: 10.1073/pnas.1313073111. Epub 2014 Jun 30.
Recently it has become apparent that N = 2 supersymmetric quantum field theory has something to do with cluster algebras. I review one aspect of the connection: supersymmetric quantum field theories have associated hyperkähler moduli spaces, and these moduli spaces carry a structure that looks like an extension of the notion of cluster variety. In particular, one encounters the usual variables and mutations of the cluster story, along with more exotic extra variables and generalized mutations. I focus on a class of examples where the underlying cluster varieties are moduli spaces of flat connections on surfaces, as considered by Fock and Goncharov [Fock V, Goncharov A (2006) Publ Math Inst Hautes Études Sci 103:1-211]. The work reviewed here is largely joint with Davide Gaiotto and Greg Moore.
最近，人们已经清楚地认识到，N=2 超对称量子场论与簇代数有关。我将回顾一下这种联系的一个方面：超对称量子场论具有相关的超凯勒模空间，而这些模空间具有一种看起来类似于簇簇变体概念扩展的结构。具体来说，人们遇到了簇故事的常见变量和突变，以及更奇特的额外变量和广义突变。我专注于一类例子，其中基础簇簇变体是平面连接的模空间表面，如 Fock 和 Goncharov [Fock V, Goncharov A (2006) Publ Math Inst Hautes Études Sci 103:1-211]所考虑的那样。这里回顾的工作主要是与 Davide Gaiotto 和 Greg Moore 合作完成的。
