引力耦合拓扑西格玛模型的关联函数之间的关系
Relations between the correlators of the topological sigma-model coupled to gravity
摘要：
我们证明了一个新的递归关系之间的关联函数$< τ_{d_1}γ_1...τ_{d_n}γ_n >_{g,β}$，它与已知的关系一起允许一个表达所有这些通过完整的系统的Gromov-Witten不变量的意义上的Kontsevich-Manin和交叉指数的重言式类$\bar{M}_{g,n}$，有效地计算鉴于早期的结果，由于芒福德，Kontsevich，Getzler和费伯。这种关系表明，大相空间坐标的线性变化将带有引力子的势变换为另一个完全根据Gromov-Witten对应和$V^n\times\bar{M}_{g,n}$上的相交理论定义的函数。然后，我们将引力后裔的形式主义从量子上同调推广到更一般的Frobenius流形和上同调场论。
英文摘要：
We prove a new recursive relation between the correlators $< τ_{d_1}γ_1...τ_{d_n}γ_n >_{g,β}$, which together with known relations allows one to express all of them through the full system of Gromov-Witten invariants in the sense of Kontsevich-Manin and the intersection indices of tautological classes on $\bar{M}_{g,n}$, effectively calculable in view of earlier results due to Mumford, Kontsevich, Getzler, and Faber. This relation shows that a linear change of coordinates of the big phase space transforms the potential with gravitational descendants to another function defined completely in terms of the Gromov-Witten correspondence and the intersection theory on $V^n\times\bar{M}_{g,n}$. We then extend the formalism of gravitational descendants from quantum cohomology to more general Frobenius manifolds and Cohomological Field Theories.
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