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 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.

Latex, 17 pages; Section 4 improved

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• The 6D SuperSwirl
• Curvature squared invariants in six-dimensional $\mathcal{N}=(1,0)$ supergravity
• A New Anomaly-Free Gauged Supergravity in Six Dimensions
• Spinorial geometry and Killing spinor equations of 6-D supergravity
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• Waves and strings in an interacting conformal chiral 2-form theory in six dimensions
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• Boosted Rotating Dyonic Strings in Salam-Sezgin Model
• On the consistency of a class of R-symmetry gauged 6D N=(1,0) supergravities
• The conformal brane-scan: an update
• The Fate of Unstable Gauge Flux Compactifications
• Spinorial geometry, horizons and superconformal symmetry in six dimensions