AI 中文总结
该研究通过非局部 $T\ar T$ 类形变的量子场论，结合热核公式分析应力张量两点函数，推导了含普适共形数据的有限引力有效作用，为诱导引力提供了量子实现。
AI 中文摘要
我们研究量子场论的非局部 $T\ar T$ 类形变在形变参数一阶下诱导产生的引力有效作用。利用热核公式，我们提取由应力张量两点函数生成的局域几何项，并将该构造应用于自由费米子、有质量麦克斯韦理论及二阶杨-米尔斯理论。尽管所得系数通常依赖于模型，但共形场理论包含由中心荷 $C_T$ 确定的普适部分。经正则化和重正化后，该部分产生由有限组曲率不变量构成的有限、与方案无关的贡献。我们进一步分析迹-迹形变，其相关接触项由外尔反常确定，并推导了一类最小非局部核对应的有限引力作用。这些结果为诱导引力提供了量子有效作用实现，其中普适共形数据决定了涌现几何响应的可计算贡献。
英文摘要
We study the gravitational effective action induced, at first order in the deformation parameter, by non-local $T\bar T$-like deformations of quantum field theories. Using a heat-kernel formulation, we extract the local geometric terms generated by stress-tensor two-point functions, and apply the construction to free fermions, massive Maxwell theory, and second-order Yang-Mills theory. While the resulting coefficients are generally model dependent, conformal field theories contain a universal sector fixed by the central charge $C_T$. After regularization and renormalization, this sector yields finite, scheme-independent contributions organized into a finite set of curvature invariants. We further analyze trace-trace deformations, for which the relevant contact terms are determined by the Weyl anomaly, and derive the corresponding finite gravitational action for a general class of minimal non-local kernels. These results provide a quantum effective-action realization of induced gravity in which universal conformal data determine calculable contributions to the emergent geometric response.
Comments43 pages, no figures
