日本京都大学Nakayama, Yu团队近日研究了非紧共形场论中的c定理及其改进。相关论文于2025年6月12日发表在《高能物理杂志》上。

一般共形场论中的能量动量张量具有改进的模糊性，它会影响推导c定理的论证。虽然Zamolodchikov的c定理的推导在改进的能量动量张量下仍然是形式上有效的，但Zamolodjikov提出的c函数的行为变得不同。当理论由于非紧性而遭受IR发散时，c函数可以是无界的，甚至可能表现出非单调性。 

然而，研究组发现，由Hartman和Mathys提出的由平均零能量条件驱动的三点函数求和规则之一，在IR理论存在缺口时，对改进是不可知的，并给出了（有效的）Virasoro中心电荷。

附：英文原文

Title: c-theorem and improvement in non-compact conformal field theories

Author: Nakamura, Nanami, Nakayama, Yu

Issue&Volume: 2025-06-12

Abstract: Energy-momentum tensor in general conformal field theories have improvement ambiguity and it can affect the argument in deriving c-theorem. While the derivation of Zamolodchikov’s c-theorem is still formally valid with the improved energy-momentum tensor, the behavior of the c-function proposed by Zamolodchikov becomes different. When the theory suffers an IR divergence due to the non-compactness, the c-function can be unbounded and may even show non-monotonicity. We find that one of the three-point function sum rule proposed by Hartman and Mathys motivated by the averaged null energy condition, however, is agnostic about the improvement and gives the (effective) Virasoro central charge, when the IR theory is gapped.

DOI: 10.1007/JHEP06(2025)119

Source: https://link.springer.com/article/10.1007/JHEP06(2025)119