标题： 共形场论的模空间和非交换黎曼几何 显示英文标题

标题： Moduli space of Conformal Field Theories and non-commutative Riemannian geometry

摘要： 我们讨论了坍塌的共形场论与具非负Ricci曲率的黎曼流形的测度Gromov-Hausdorff极限之间的类比。 受此启发，我们提出了“非交换”的（“量子”）黎曼d几何的概念。 我们解释了当d=1时这种结构如何与Connes的谱三元组相关联。 在附录中，基于与Maxim Kontsevich的合作研究（未发表），我们讨论了量子场论的形变理论以及当时空为任意紧致度量空间时的量子场论方法。 显示英文摘要

摘要： We discuss the analogy between collapsing Conformal Field Theories and measured Gromov-Hausdorff limit of Riemannian manifolds with non-negative Ricci curvature. Motivated by this analogy we propose the notion of non-commutative (``quantum") Riemannian d-geometry. We explain how this structure is related to Connes's spectral triples in the case d=1. In the Appendix based on the unpublished joint work with Maxim Kontsevich we discuss deformation theory of Quantum Field Theories as well as an approach to QFTs in the case when the space-time is an arbitrary compact metric space.