局部泛函的非重整化定理：在与动态几何耦合的无鬼向量场理论中
A Non-Renormalization Theorem for Local Functionals in Ghost-Free Vector Field Theories Coupled to Dynamical Geometry
AI总结：
本文证明了在与动态几何耦合的无鬼向量场理论中，经典相互作用在重整化下保持稳定，量子修正不会引入新的局部相互作用。
摘要：
我们为一类描述与动态几何耦合的有质量向量场理论的局部泛函建立了非重整化定理。在局部性、洛伦兹不变性和有效场论展开在固定截止值以下有效性的假设下，我们证明量子修正不会生成局部算符，这些算符会重整化经典导数自相互作用，这些自相互作用负责理论的约束结构。证明结合了允许局部抵消项空间的算符级分析与系统性的脱耦极限论证，该论证在导数展开的每一阶中分离了有效作用的主要贡献。结果是，所有由辐射引起的局部泛函必然包含每个场的额外导数，并被理论内在的强耦合尺度所抑制。特别是，定义无鬼向量场理论的经典相互作用在重整化下是稳定的，任何由量子修正产生的额外自由度只出现在有效场论截止值之上。这一结果将已知的平坦空间向量理论的非重整化性质扩展到动态几何的情况，并提供了其对所有环次的微扰稳定性结构解释。
英文摘要：
We establish a non-renormalization theorem for a class of ghost-free local functionals describing massive vector field theories coupled to dynamical geometry. Under the assumptions of locality, Lorentz invariance, and validity of the effective field theory expansion below a fixed cutoff, we show that quantum corrections do not generate local operators that renormalize the classical derivative self-interactions responsible for the constraint structure of the theory. The proof combines an operator-level analysis of the space of allowed local counterterms with a systematic decoupling-limit argument, which isolates the leading contributions to the effective action at each order in the derivative expansion. As a consequence, all radiatively induced local functionals necessarily involve additional derivatives per field and are suppressed by the intrinsic strong-coupling scales of the theory. In particular, the classical interactions defining ghost-free vector field theories are stable under renormalization, and any additional degrees of freedom arising from quantum corrections appear only above the effective field theory cutoff. This result extends known non-renormalization properties of flat-space vector theories to the case of dynamical geometry and provides a structural explanation for their perturbative stability to all loop orders.
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