Bertotti-Robinson type solutions to Dilaton-Axion Gravity

Abstract

We present a new solution to dilaton-axion gravity which looks like a rotating Bertotti-Robinson (BR) Universe. It is supported by an homogeneous Maxwell field and a linear axion and can be obtained as a near-horizon limit of extremal rotating dilaton-axion black holes. It has the isometry \(SL(2,R)\times U(1)\) where U(1) is the remnant of the SO(3) symmetry of BR broken by rotation, while \(SL(2,R)\) corresponds to the \(AdS_2\) sector which no longer factors out of the full spacetime. Alternatively our solution can be obtained from the D=5 vacuum counterpart to the dyonic BR with equal electric and magnetic field strengths. The derivation amounts to smearing it in D=6 and then reducing to D=4 with dualization of one Kaluza-Klein two-form in D=5 to produce an axion. Using a similar dualization procedure, the rotating BR solution is uplifted to D=11 supergravity. We show that it breaks all supersymmetries of N=4 supergravity in D=4, and that its higher dimensional embeddings are not supersymmetric either. But, hopefully it may provide a new arena for corformal mechanics and holography. Applying a complex coordinate transformation we also derive a BR solution endowed with a NUT parameter.