论文标题
Feynman积分的大量保形对称性和一体性
Massive Conformal Symmetry and Integrability for Feynman Integrals
论文作者
论文摘要
在平面全息图的背景下，整合性在解决某些无质量量子场理论（例如n = 4 sym理论）方面起着重要作用。在这封信中，我们表明，集成性还具有大量量子场理论的构建基础。在一环订单下，我们证明了通用时空维度中的所有大型N-GON FEYNMAN积分在大规模的桑对称性下都是不变的。在两个循环中，可以证明相似的陈述可以证明由两个n gon构建的图形。在通用循环顺序下，我们猜测所有图形都从平面的常规瓷砖上切出，边界上的大量传播器都是不变的。我们通过许多数值测试来支持这种猜想，以实现更高的回路和腿部。观察到的仰光扩展了十年前在n = 4 sym理论的库仑分支上发现的巨大双重形式对称性的骨气部分。通过将Yangian水平的发电机从双重动量空间转换为原始动量空间，我们引入了动量空间共形对称性的大规模概括。即使对于非对偶发性积分，这种新颖的对称性仍然存在。因此，扬吉亚人可以理解为闭合大规模的双重形式对称性和这种新的大型动量空间形成型对称性，这暗示了通过ADS/CFT进行解释。为了应用我们的发现，我们引导超几何构建块，以获取大量Feynman积分的示例。
In the context of planar holography, integrability plays an important role for solving certain massless quantum field theories such as N=4 SYM theory. In this letter we show that integrability also features in the building blocks of massive quantum field theories. At one-loop order we prove that all massive n-gon Feynman integrals in generic spacetime dimensions are invariant under a massive Yangian symmetry. At two loops similar statements can be proven for graphs built from two n-gons. At generic loop order we conjecture that all graphs cut from regular tilings of the plane with massive propagators on the boundary are invariant. We support this conjecture by a number of numerical tests for higher loops and legs. The observed Yangian extends the bosonic part of the massive dual conformal symmetry that was found a decade ago on the Coulomb branch of N=4 SYM theory. By translating the Yangian level-one generators from dual to original momentum space, we introduce a massive generalization of momentum space conformal symmetry. Even for non-dual conformal integrals this novel symmetry persists. The Yangian can thus be understood as the closure of massive dual conformal symmetry and this new massive momentum space conformal symmetry, which suggests an interpretation via AdS/CFT. As an application of our findings, we bootstrap the hypergeometric building blocks for examples of massive Feynman integrals.
