Interacting string multi-verses and holographic instabilities of massive gravity

Products of large-N   conformal field theories coupled by multi-trace interactions in diverse dimensions are used to define quantum multi-gravity (multi-string theory) on a union of (asymptotically) AdS spaces. One-loop effects generate a small O(1/N)O(1/N) mass for some of the gravitons. The boundary gauge theory and the AdS/CFT correspondence are used as guiding principles to study and draw conclusions on some of the well-known problems of massive gravity – classical instabilities and strong coupling effects. We find examples of stable multi-graviton theories where the usual strong coupling effects of the scalar mode of the graviton are suppressed. Our examples require a fine tuning of the boundary conditions in AdS. Without it, the spacetime background backreacts in order to erase the effects of the graviton mass.