近日，日本京都大学Nguyen, Ung团队报道了用ANEC重温k定理。2026年3月23日出版的《高能物理杂志》发表了这项成果。

二维重正化群流的基本定理是c-定理，它表明自由度数目必须沿重正化群流单调递减。而k-定理则声称带电荷的自由度数目也呈单调递减，其中k是由电流两点函数定义的电流中心荷。

Hartman与Mathys近期利用三点函数求和规则以及平均零能量（ANE）算子的正定性推导了c-定理，这促使学界寻求类似方法证明k-定理。对于k-定理的情况，需要考虑部分接触项的影响。忽略部分接触项会得到矛盾的结果，而研究组在仔细分析后将部分接触项纳入考量，从而获得了正确的求和规则，并基于ANE算子的正定性给出了完整证明。

附：英文原文

Title: Revisiting the k-theorem with the ANEC

Author: Nakamura, Nanami, Nakayama, Yu, Nguyen, Ung

Issue&Volume: 2026-03-23

Abstract: The fundamental theorem in renormalization group flows in two dimensions is the c-theorem, which dictates that the number of degrees of freedom must decrease monotonically along the renormalization group flow. The k-theorem claims that the number of charged degrees of freedom also decreases monotonically. Here, k is the current central charge defined by the two-point function of the current. A recent derivation of the c-theorem by Hartman and Mathys, which uses the three-point function sum rule and the positivity of the averaged null energy (ANE) operator, motivates us to seek a similar proof of the k-theorem. In the case of the k-theorem, the partial contact terms need to be taken into consideration. While ignoring the partial contact terms yields contradictory results, our careful analysis incorporating them leads to the correct sum rule and a complete proof based on the positivity of the ANE operator.

DOI: 10.1007/JHEP03(2026)209

Source: https://link.springer.com/article/10.1007/JHEP03(2026)209