近日，美国宾夕法尼亚州立大学的Mark Alaverdian与美国普林斯顿高等研究院的Aidan Herderschee合作，推导出维滕图的差分方程和积分族。相关研究成果已于2024年12月10日在国际知名学术期刊《高能物理杂志》上发表。

该研究团队表明，反德西特空间中的树级和单圈梅林空间相关函数，遵循特定的差分方程，这些方程是平坦空间中费曼圈积分微分方程的直接类比。

研究人员推导出了有限差分关系，称之为“分部求和关系”，它与费曼圈积分的分部积分关系相类似，用于将积分化简至一个基。

研究人员通过明确推导出各种树级，和单圈维滕图（直至四点泡泡图）的差分方程和分部求和关系，来阐述这一通用方法。

附：英文原文

Title: Difference equations and integral families for Witten diagrams

Author: Alaverdian, Mark, Herderschee, Aidan, Roiban, Radu, Teng, Fei

Issue&Volume: 2024-12-10

Abstract: We show that tree-level and one-loop Mellin space correlators in anti-de Sitter space obey certain difference equations, which are the direct analog to the differential equations for Feynman loop integrals in the flat space. Finite-difference relations, which we refer to as “summation-by-parts relations”, in parallel with the integration-by-parts relations for Feynman loop integrals, are derived to reduce the integrals to a basis. We illustrate the general methodology by explicitly deriving the difference equations and summation-by-parts relations for various tree-level and one-loop Witten diagrams up to the four-point bubble level.

DOI: 10.1007/JHEP12(2024)070

Source: https://link.springer.com/article/10.1007/JHEP12(2024)070