AI 中文总结
本文针对闭实解析凯勒流形上全纯场论的费曼图积分，证明其在三种重整化方案下收敛且结果一致，基于代数几何奇妙紧化理论建立了这类积分的规范反常公式。
AI 中文摘要
费曼图积分的发散是微扰量子场论研究的核心问题之一，这类积分的严格表述通常需要重整化。本文证明，来自闭实解析凯勒流形上全纯场论的费曼图积分，相对于热核重整化、柯西主值重整化和ζ函数重整化是收敛的，且这三种重整化方案给出相同结果。我们的证明基于代数几何中的奇妙紧化理论，该理论为这类积分提供了几何理解，由此建立了这些图积分的规范反常公式。
英文摘要
The divergence of Feynman graph integrals is one of the central issues in the study of perturbative quantum field theories. A rigorous formulation of these integrals usually requires renormalization. In this paper, we prove that the Feynman graph integrals arising from holomorphic field theories on closed real-analytic Kähler manifolds are convergent with respect to heat-kernel renormalization, Cauchy principal value renormalization, and zeta-function renormalization. Moreover, these three renormalization procedures produce the same value. Our proof is based on the theory of wonderful compactifications in algebraic geometry, which provides a geometric understanding of these integrals. As a consequence, we establish a gauge anomaly formula for these graph integrals.
Comments82 pages, 0 figures. Fixed `\Cref` cross-reference issues caused by a compiler-version incompatibility. Comments are welcome
