A 4d non-BPS NS-NS microstate

Abstract We construct a two-parameter four-dimensional non-BPS NS-NS smooth microstate solution that asymptotes to flat spacetime with a linear dilaton in type II superstring theory. From the microscopic point of view, the background is made out of a certain number of decoupled (i.e. g_s → 0) NS5 branes wrapping T³ x S¹ x S¹ with fundamental strings wrapping non-contractable cycles of S¹ x S¹ with integer momentum modes along them. We show that perturbative worldsheet theory in this background is given by a null-gauged WZW model. We also show that the consistency of the worldsheet theory imposes non-trivial constraints on the supergravity background.