摘要翻译：
我们提出了一个Hodge场论结构，它抓住了Zwiebach不变量约简为Gromov-Witten不变量的代数性质。将Barannikov-Kontsevich构式推广到具有引力后代的高属相关子的情形。我们证明了代数定义的Hodge场论相关子满足所有重言式关系的主要定理。从这个角度看，Barannikov-Kontsevich构造提供WDVV方程解的陈述看起来是我们定理的最简单的特例。并推广了我们以前工作中证明的其它低属重言式关系的特例；我们用新的概念证明代替了旧的技术证明。
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英文标题：
《Tautological relations in Hodge field theory》
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作者：
A. Losev, S. Shadrin, I. Shneiberg
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最新提交年份：
2007
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分类信息：

一级分类：Mathematics        数学
二级分类：Quantum Algebra        量子代数
分类描述：Quantum groups, skein theories, operadic and diagrammatic algebra, quantum field theory
量子群，skein理论，运算代数和图解代数，量子场论
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一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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英文摘要：
  We propose a Hodge field theory construction that captures algebraic properties of the reduction of Zwiebach invariants to Gromov-Witten invariants. It generalizes the Barannikov-Kontsevich construction to the case of higher genera correlators with gravitational descendants.   We prove the main theorem stating that algebraically defined Hodge field theory correlators satisfy all tautological relations. From this perspective the statement that Barannikov-Kontsevich construction provides a solution of the WDVV equation looks as the simplest particular case of our theorem. Also it generalizes the particular cases of other low-genera tautological relations proven in our earlier works; we replace the old technical proofs by a novel conceptual proof.
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PDF链接：
https://arxiv.org/pdf/0704.1001