Title: On the renormalization of massive vector field theory coupled to scalar in curved space-time Show Chinese title

Title: 关于与标量场在弯曲时空耦合的 massive 向量场理论的重整化

Abstract: We consider the renormalization of massive vector field interacting with charged scalar field in curved spacetime. Starting with the theory minimally coupled to external gravity and using the formulations with and without St\"uckelberg fields, we show that the longitudinal mode of vector field is completely decoupled and the remaining theory of transverse vector field is renormalizable by power counting. The formal arguments based on the covariance and power counting indicate that multiplicative renormalizability of the interacting theory may require introducing two non-minimal terms linear in Ricci tensor in the vector sector. Nevertheless, a more detailed analysis shows that these non-minimal terms violate the decoupling of the longitudinal mode and are prohibited. As a verification of general arguments, we derive the one-loop divergences in the minimal massive scalar QED, using St\"uckelberg procedure and the heat-kernel technique. The theory without non-minimal terms proves one-loop renormalizable and admits the renormalization group equations for all the running parameters in the scalar and vector sectors. One-loop beta functions do not depend on the gauge fixing and can be used to derive the effective potential. Show Chinese abstract

Abstract: 我们研究了具有曲率时空中的带电标量场相互作用的有质量矢量场的重整化问题。从外部引力最小耦合的理论出发，并利用包含和不包含施特克尔贝格场的表述方法，我们证明矢量场的纵向模完全解耦，剩余的横向矢量场理论通过计数幂次是可以重整化的。基于协变性和计数幂次的正式论证表明，相互作用理论的乘法重整化可能需要在矢量部分引入两个线性于黎曼张量的非最小项。然而，更详细的分析显示这些非最小项违反了纵向模的解耦，并且是被禁止的。作为一般论证的验证，我们使用施特克尔贝格过程和热核技术，在最小有质量标量QED中推导出一阶发散项。没有非最小项的理论证明是一阶可重整化的，并且允许标量和矢量部分的所有运行参数的重正化群方程。一阶β函数不依赖于规范固定并且可以用来推导有效势能。