Product CFTs, gravitational cloning, massive gravitons and the space of gravitational duals

TL;DR

The work addresses whether multiple interacting gravitons can arise in AdS/CFT by forming products of large-N CFTs and coupling them with double-trace perturbations, yielding bulk duals that are product geometries with a shared boundary. It shows that at most one interacting massless graviton can persist, while additional gravitons become massive with masses suppressed as ${m_{ m graviton}^2 \sim 1/(N^2 \ell_{AdS}^2)}$, and that the spectrum and interactions can be analyzed via a generalized GKPW framework with coupled boundary conditions. The paper provides explicit 4D and 2D examples, including a nonperturbative instability in a two ${\cal N}=4$ SYM setup and a marginal, diagonal-breaking deformation between two ${\cal N}=1$ $T^{1,1}$ conifold theories, and discusses the broader implications for the space of gravitational duals and multi-graviton dynamics. It concludes by outlining a cobordism-like structure of dual geometries, the feasibility of higher-junctions in various dimensions, and several open questions on finite-temperature behavior and black-hole physics in these coupled systems.

Abstract

The question of graviton cloning in the context of the bulk/boundary correspondence is considered. It is shown that multi-graviton theories can be obtained from products of large-N CFTs. No more than one interacting massless graviton is possible. There can be however, many interacting massive gravitons. This is achieved by coupling CFTs via multi-trace marginal or relevant perturbations. The geometrical structure of the gravitational duals of such theories is that of product manifolds with their boundaries identified. The calculational formalism is described and the interpretation of such theories is discussed.