渐近外尔不变引力中的紫外封闭性
Ultraviolet Closure in Asymptotically Weyl-Invariant Gravity
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中文总结 AI 辅助
该研究分析渐近外尔不变引力（AWIG）的紫外行为，通过帕拉蒂尼形式确定其紫外端点为R²作用量，发现其紫外发散抵消项具有特殊结构，为改进爱因斯坦引力的紫外性质提供了证据。
中文摘要 AI 辅助
我们研究帕拉蒂尼形式下的渐近外尔不变引力（AWIG），其由指数n插值，当n趋近于1时对应类爱因斯坦的红外 regime，当n趋近于2时对应外尔不变的紫外 regime。在四维空间中，我们证明在极小标量帕拉蒂尼f(R)扇区内的严格外尔不变性，唯一地将R²作用量选为紫外端点。将该指数解释为依赖曲率的有效量，我们约束了一类符合所需红外和紫外端点的平滑自治流的唯象类。随后我们分析严格紫外理论：在正则分支R≠0，且在由曲率纯构造的受限无挠、宇称偶扇区内，所有容许的发散壳上抵消项在任意圈阶均约化为原始的√(-g)R²项加上拓扑欧拉密度。尽管该条件性结果未确立完整的壳外微扰可重整性，但它提供了相对于爱因斯坦引力更优紫外行为的非平凡证据，并为未来第一性原理重整化群计算确定了具体目标。
英文摘要
We investigate asymptotically Weyl-invariant gravity (AWIG) in the Palatini formulation, defined by an exponent n that interpolates between an Einstein-like infrared regime, where n goes to one, and a Weyl-invariant ultraviolet regime, where n goes to two. In four dimensions, we show that exact Weyl invariance within the minimal scalar Palatini f(R) sector uniquely selects the R^2 action as the ultraviolet endpoint. Interpreting the exponent as an effective curvature-dependent quantity, we constrain a phenomenological class of smooth autonomous flows compatible with the required infrared and ultraviolet endpoints. We then analyse the strict ultraviolet theory. On the regular branch R not equal to zero, and within a restricted torsionless, parity-even sector constructed purely from curvature, all admissible divergent on-shell counterterms reduce at arbitrary loop order to the original \sqrt{-g}R^2 term plus a topological Euler density. Although this conditional result does not establish full off-shell perturbative renormalizability, it provides nontrivial evidence for improved ultraviolet behaviour relative to Einstein gravity and identifies a concrete target for a future first-principles renormalization-group calculation.
发表机构
- The Niels Bohr Institute, University of Copenhagen（哥本哈根大学尼尔斯玻尔研究所）
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