探索渐近安全的单模量子引力的新角落
Exploring new corners of asymptotically safe unimodular quantum gravity
摘要：
在流动有效作用量的两类不同截断下研究么模量子引力的重整化群流。特别是，我们寻找非平凡的不动点解的多项式展开的$f(R)$型以及$F(R_{μν}R^{μν})+R\,Z(R_{μν}R^{μν})$家庭的最大对称背景。我们关闭系统的β函数的引力耦合与异常尺寸的引力子和Faddeev-Popov鬼治疗根据两个独立的处方：一个基于所谓的背景近似和其他的基础上的混合方法相结合的背景近似与同时顶点和导数扩展。为了一致性，在背景近似，我们采用了一个背景相关的校正流方程所产生的单模路径积分的功能性措施的适当治疗。我们还研究了调节器函数中自同态参数的不同正则选择如何影响不动点结构。虽然我们已经找到了证据证明存在一个非平凡的不动点的两类多项式投影，$f(R)$截断表现出更好的（明显的）收敛性能。此外，我们认为包含的物质领域没有自相互作用最低限度地耦合到么模引力作用，我们发现的证据渐近安全的么模量子引力与标准模型和它的一些常见的扩展的字段内容的兼容性。
英文摘要：
The renormalization group flow of unimodular quantum gravity is investigated within two different classes of truncations of the flowing effective action. In particular, we search for non-trivial fixed-point solutions for polynomial expansions of the $f(R)$-type as well as of the $F(R_{μν}R^{μν})+R\,Z(R_{μν}R^{μν})$ family on a maximally symmetric background. We close the system of beta functions of the gravitational couplings with anomalous dimensions of the graviton and Faddeev-Popov ghosts treated according to two independent prescriptions: one based on the so-called background approximation and the other based on a hybrid approach which combines the background approximation with simultaneous vertex and derivative expansions. For consistency, in the background approximation, we employ a background-dependent correction to the flow equation which arises from the proper treatment of the functional measure of the unimodular path integral. We also investigate how different canonical choices of the endomorphism parameter in the regulator function affect the fixed-point structure. Although we have found evidence for the existence of a non-trivial fixed point for the two classes of polynomial projections, the $f(R)$ truncation exhibited better (apparent) convergence properties. Furthermore, we consider the inclusion of matter fields without self-interactions minimally coupled to the unimodular gravitational action and we find evidence for compatibility of asymptotically safe unimodular quantum gravity with the field content of the Standard Model and some of its common extensions.
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