Doubly-fluctuating BPS solutions in six dimensions

A bstract We analyze the BPS solutions of minimal supergravity coupled to an anti-self-dual tensor multiplet in six dimensions and find solutions that fluctuate non-trivially as a function of two variables. We consider families of solutions coming from KKM monopoles fibered over Gibbons-Hawking metrics or, equivalently, non-trivial T 2 fibrations over an base. We find smooth microstate geometries that depend upon many functions of one variable, but each such function depends upon a different direction inside the T 2 so that the complete solution depends non-trivially upon the whole T 2 . We comment on the implications of our results for the construction of a general superstratum.