Fine Tuning and Six-Dimensional Gauged $N=(1,0)$ Supergravity Vacua

TL;DR

This paper discovers a new family of supersymmetric AdS_3 x S^3 vacua in six-dimensional gauged N=(1,0) supergravity, characterized by a freely adjustable squashing of the S^3, and explores related dyonic string solutions.

Contribution

It introduces a novel family of supersymmetric vacua with adjustable squashing in six-dimensional supergravity, expanding understanding of vacuum solutions and their relation to known Minkowski backgrounds.

Findings

New family of supersymmetric AdS_3 x S^3 vacua with squashed S^3

The vacua are supersymmetric for all squashing parameters

Near-horizon limits of dyonic strings approach these 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 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.