Analytic Structure of all Loop Banana Amplitudes

主讲人:Albrecht Klemm
时间: 15:30-16:30, Friday 2020-9-25
地点:Zoom ID: 557 931 1626 Passcode: 758063


Abstract: Using the Gelfand-Kapranov-Zelevinsk\u{\i} system for the primitive Cohomology of an infinite series of complete intersection Calabi-Yau manifolds, whose dimension is the loop order minus one, we completely clarify the analytic structure of all banana amplitudes with arbitrary masses. In particular, we find that the leading logarithmic structure in the high energy regime, which corresponds to the point of maximal unipotent monodromy, is determined by a novel $\widehat \Gamma$-class evaluation in the ambient spaces of the mirror, while the imaginary part of the amplitude in this regime is determined by the $\widehat \Gamma$-class of the mirror Calabi-Yau manifold itself. We provide simple closed all loop formulas for the former as well as for the Frobenius $\kappa$-constants, which determine the behaviour of the amplitudes, when the momentum square equals the sum of the masses squared, in terms of zeta values. We extend our previous work from three to four loops by providing for the latter case a complete set of (inhomogenous) Picard-Fuchs differential equations for arbitrary masses. This allows to evaluate the amplitude as well as other master integrals with raised powers of the propagators in very short time to very high numerical precision for all values of the physical parameters. Using a recent $p$-adic analysis of the periods we determine the value of the maximal cut equal mass four-loop amplitude at the attractor points in terms of periods of modular weight two and four Hecke eigenforms and the quasiperiods of their meromorphic cousins


报告人简介: Albrecht Klemm教授,德国波恩大学物理系教授。1990年于德国海德堡大学获得博士学位,之后于慕尼黑大学,哈佛大学,欧洲核子中心等地从事博士后研究。1998-2000年,获得海森堡基金到普林斯顿高等研究院从事研究。先后在柏林洪堡大学,威斯康星大学麦迪逊分校任职,目前任职于波恩大学。Klemm教授主要致力于超弦理论的研究,尤其在Gromov-Witten理论,镜像对称,弦论/规范理论对偶领域有着突出贡献。他和他的合作者提出的topological vertextopological recursion方法,已经成为该领域广泛应用的工具。他们利用镜像对称和模性质,得到了紧致卡拉比–丘流形的高亏格Gromov-Witten不变量。目前已经发表一百篇余篇国际论文,引用逾8000次,学术专著包括“Mirror Symmetry”,“B-Model Gromov-Witten Theory”等。

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