Fine tuning and six-dimensional gauged N = (1,0) supergravity vacua

We find a new family of supersymmetric vacuum solutions in the six-dimensional chiral gauged N = (1,0) supergravity theory. They are generically of the form AdS(3) x S-3, where the 3-sphere is squashed homogeneously along its Hopf fibres. The squashing is freely adjustable, corresponding to changing the 3-form charge, and the solution is supersymmetric for all squashings. In a limit where the length of the Hopf fibres goes to zero, one recovers, after a compensating rescaling of the fibre coordinate, a solution that is locally the same as the well-known (Minkowski)(4) x S-2 vacuum of this theory. It can now be viewed as a fine tuning of the new more general family. The traditional 'cosmological constant problem' is replaced in this theory by the problem of why the four-dimensional (Minkowski)(4) x S-2 vacuum should be selected over other members of the equally supersymmetric AdS(3) x S-3 family. We also obtain a family of dyonic string solutions in the gauged N = (1, 0) theory, whose near-horizon limits approach the AdS(3) times squashed S-3 solutions.