辛不变量、维拉索罗约束和Givental分解
Symplectic invariants, Virasoro constraints and Givental decomposition
摘要：
根据Alexandrov，Mironov和Morozov的工作，我们证明了从给定的谱曲线建立的\cite{EOinvariants}的辛不变量满足一组与微分形式$ydx$的每个极点和$dx$的每个零点相关的维拉索罗约束。然后，我们表明，他们满足相同的限制，配分函数的矩阵M-理论定义的亚历山德罗夫，米罗诺夫和Morozov。该理论的不同矩阵模型之间的对偶性作为辛不变量之间的对偶性的一种特殊情况而被清楚地阐明。事实上，辛不变量允许两种分解：一方面作为Kontsevich积分的乘积，另一方面作为1个厄米矩阵积分的乘积。这两个分解可以看作是KPTau函数的Givental公式。
英文摘要：
Following the works of Alexandrov, Mironov and Morozov, we show that the symplectic invariants of \cite{EOinvariants} built from a given spectral curve satisfy a set of Virasoro constraints associated to each pole of the differential form $ydx$ and each zero of $dx$ . We then show that they satisfy the same constraints as the partition function of the Matrix M-theory defined by Alexandrov, Mironov and Morozov. The duality between the different matrix models of this theory is made clear as a special case of dualities between symplectic invariants. Indeed, a symplectic invariant admits two decomposition: as a product of Kontsevich integrals on the one hand, and as a product of 1 hermitian matrix integral on the other hand. These two decompositions can be though of as Givental formulae for the KP tau functions.
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