Supergravity flows, wormholes and their pseudo-Hermitian holographic duals

We find solutions to consistent truncations of supergravity where some real scalars are analytically extended to imaginary values, ensuring the metric remains real-valued. Among the solutions there are Lorentzian traversable wormholes connecting two asymptotically Anti-de Sitter spacetimes and flows that have a real metric also when uplifted to ten or eleven dimensions. We argue that the holographic duals are pseudo-Hermitian and $PT$-symmetric theories. Wormhole solutions also admit an interpretation as the low-energy theory of two stacks of branes and antibranes after tachyon condensation. The wormhole is then dual to an entangled state of two copies of the theory that lives on a stack of branes. We present some evidence by computing the mutual information between the theories at each boundary and by identifying the Goldstone bosons associated to the breaking of the two copies of Poincar\'e symmetry to their diagonal subgroup.