Decoupling Supergravity from the Superstring

We consider the conditions necessary for obtaining perturbative maximal supergravity in d dimensions as a decoupling limit of type II superstring theory compactified on a (10 − d)-torus. For dimensions d = 2 and d = 3 it is possible to define a limit in which the only finite-mass states are the 256 massless states of maximal supergravity. However, in dimensions d ≥ 4 there are infinite towers of additional massless and finitemass states. These correspond to Kaluza–Klein charges, wound strings, Kaluza–Klein monopoles or branes wrapping around cycles of the toroidal extra dimensions. We conclude that perturbative supergravity cannot be decoupled from string theory in dimensions ≥ 4. In particular, we conjecture that pure N = 8 supergravity in four dimensions is in the Swampland.