标题： 四维量子引力理论的共形和非共形显式解 显示英文标题

标题： A Four-Dimensional Theory for Quantum Gravity with Conformal and Nonconformal Explicit Solutions

摘要： 该理论最一般的形式是对应于弯曲时空中的无维高阶导数标量场模型的可重整化$d=4$理论。 该理论的经典作用量包含$12$个独立函数，这些是该理论的广义耦合常数。 我们计算了一环beta函数，然后考虑了有限性的条件。 证明了幂次类型的精确解集恰好由三个共形解和三个非共形解组成，这些解由我们明确得到的显著简单的（尽管是非平凡的）函数构成。 共形理论的有限性表明在有限部分中不存在共形异常。 研究了有限解的稳定性，并讨论了重整化群流的可能性以及几种物理应用。 显示英文摘要

摘要： The most general version of a renormalizable $d=4$ theory corresponding to a dimensionless higher-derivative scalar field model in curved spacetime is explored. The classical action of the theory contains $12$ independent functions, which are the generalized coupling constants of the theory. We calculate the one-loop beta functions and then consider the conditions for finiteness. The set of exact solutions of power type is proven to consist of precisely three conformal and three nonconformal solutions, given by remarkably simple (albeit nontrivial) functions that we obtain explicitly. The finiteness of the conformal theory indicates the absence of a conformal anomaly in the finite sector. The stability of the finite solutions is investigated and the possibility of renormalization group flows is discussed as well as several physical applications.