On the mass spectrum of Viel-dreibein gravity

Abstract

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.