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

Abstract

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 × 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 × 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 × S 2 vacuum should be selected over other members of the equally supersymmetric AdS 3 × 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.

More anomaly free models of six-dimensional gauged supergravity

“…Hence in our case, 3 See [20] for the models with monopoles sitting in the U (1) factor, and [21] for those with monopoles sitting in the nonabelian factor. 4 Note that in six dimensions the consistency of the Green-Schwarz mechanism is rather subtle, because we need to modify the lowest-derivative terms in the Lagrangian in order to introduce the Green-Schwarz counterterm. More details can be found in references [2,22], including the generalization to n T > 1.…”

“…The gauged one is particularly interesting, because it does not allow the flat six-dimensional Minkowski spacetime as a solution. Their solutions typically describe spacetimes which are spontaneously compactified to lower dimensions [3,4]. They can also be used to build various higher-dimensional models of particle phenomenology and cosmology.…”

The 6D superswirl

“…For example, by considering different space-time factorisations, the authors of [19] determined solutions of the form AdS 3 × S 3 , as well as dyonic string configurations; generalisations of the latter have been found in [14].…”

“…In order to compute this, we need the values of the space-time spin connection. For example, when the non-compact directions are Minkowski g µν = η µν , the nonzero components are given by: 19) whereμ and q(q) are flat indices. Assuming that the spinor ǫ is a function only of z,z, from the M = µ component of the gravitino equation; 20) we can see that, for a 4D Minkowski solution,…”

Variant = (1,1) supergravity and (Minkowski) 4 × S 2 vacua

“…This self-tuning mechanism has been highlighted recently in [2,3] where it was noted that the four-dimensional cosmological constant is protected against large contributions in a Salam-Sezgin braneworld scenario, even after supersymmetry breaking on the branes. (Note, however, that this self-tuning presupposes the existence of a (Minkowski) 4 vacuum to start with [4].) The S 2 reduction of the Salam-Sezgin model was recently examined in [5], and its lower dimensional spectrum was analyzed.…”