AI 中文总结
本文研究三维多引力理论Viel-dreibein引力的AdS波构型，通过将系统重写为高阶导数理论并因式分解方程，确定其质量谱，发现临界点处平方质量简并范围更广及对数模式等特性，为相关研究提供关键基础。
AI 中文摘要
我们研究Viel-dreibein引力的AdS波构型，该理论是包含N个相互作用自旋-2场的三维理论，以此为背景来表征这个多引力理论的质量谱。我们成功采用已知策略，将该系统重写为单个dreibein的高阶导数理论，从而推导出描述所讨论AdS波轮廓动力学的精确2N阶方程。我们引入的第二个创新点是将该方程因式分解为N个克莱因-戈登算子的乘积，这利用了近期用日益知名的$\nobreakdash\backslashmathscr{A}$-超几何函数表示任意N次多项式根的方法。值得注意的是，这使我们能够确定整个理论的质量谱，且与涉及的引力数量无关，这对AdS波解的显式构建至关重要。这让我们能够探索该理论的参数空间，找到其所有临界点（不仅是Breitenlohner-Freedman界），在这些点上平方质量的简并范围要大得多。在这些点上，解允许出现大量新的对数模式，产生多种$\nobreakdash\backslash log^{\nobreakdash\backslash chi-1}$渐近行为，其中$\nobreakdash\backslash chi\nobreakdash\backslash le N$，这是存在所谓对偶对数共形场论的标志。
英文摘要
We study the AdS-wave configurations of Viel-dreibein gravity, a three-dimensional theory of $N$ interacting spin-2 fields, as a pretext to characterize the mass spectrum of this multigravity theory. We manage to implement the known strategy of rewriting the system as a higher-derivative theory for a single dreibein, thereby deriving the precise $2N$th-order equation governing the dynamics of the AdS-wave profile in question. The second novelty we introduce is a factorization of such an equation as the product of $N$ Klein-Gordon operators, exploiting the recent representation of the roots of any $N$th-degree polynomial in terms of the increasingly celebrated $\mathscr{A}$-hypergeometric functions. Remarkably, this allows us to determine the mass spectrum of the full theory independently of the number of involved gravities, which is essential for an explicit construction of the AdS-wave solutions. This enables us to explore the parameter space of the theory and find all its critical points (not only the Breitenlohner-Freedman bounds) where a much wider range of degeneracies in the squared masses arises. At those points, the solutions allow a zoo of new logarithmic modes leading to several $\log^{χ-1}$ asymptotic behaviors, with $χ\le N$, a signature of the existence of allegedly dual logarithmic conformal field theories.
Comments43 pages
