Vertex algebras of CohFT-type
Vertex algebras of CohFT-type
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发表时间：
2019-10
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通讯作者：
Chiara Damiolini;A. Gibney;Nicola Tarasca
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作者：
Chiara Damiolini;A. Gibney;Nicola Tarasca
某些顶点代数的表示，这里称为CohFT型，可以用来构造稳定曲线的模空间上的共形块和共不变向量丛[DGT2]。我们表明，这种束定义半单上同调场论。作为应用，我们按照[MOPPZ]中关于仿射李代数上可积模给出的丛的方法和计算，给出了它们的全Chern特征标的融合规则表达式.由此可见，陈省身类是重言式的。实例和开放的问题进行了讨论。
Representations of certain vertex algebras, here called of CohFT-type, can be used to construct vector bundles of coinvariants and conformal blocks on moduli spaces of stable curves [DGT2]. We show that such bundles define semisimple cohomological field theories. As an application, we give an expression for their total Chern character in terms of the fusion rules, following the approach and computation in [MOPPZ] for bundles given by integrable modules over affine Lie algebras. It follows that the Chern classes are tautological. Examples and open problems are discussed.