Towards a Naturally Small Cosmological Constant from Branes in 6D Supergravity

TL;DR

This paper explores a 6D supergravity model where branes can self-tune the effective 4D cosmological constant to a small value, potentially explaining dark energy and linking it to observable effects in gravity tests.

Contribution

It demonstrates a classical self-tuning mechanism in 6D supergravity with branes, and analyzes an explicit anomaly-free model with partial success due to topological constraints.

Findings

3-branes can remain classically flat regardless of tension

Self-tuning may be stabilized by bulk supersymmetry

Explicit model shows partial realization of the mechanism

Abstract

We investigate the possibility of self-tuning of the effective 4D cosmological constant in 6D supergravity, to see whether it could naturally be of order 1/r^4 when compactified on two dimensions having Kaluza-Klein masses of order 1/r. In the models we examine supersymmetry is broken by the presence of non-supersymmetric 3-branes (on one of which we live). If r were sub-millimeter in size, such a cosmological constant could describe the recently-discovered dark energy. A successful self-tuning mechanism would therefore predict a connection between the observed size of the cosmological constant, and potentially observable effects in sub-millimeter tests of gravity and at the Large Hadron Collider. We do find self tuning inasmuch as 3-branes can quite generically remain classically flat regardless of the size of their tensions, due to an automatic cancellation with the curvature and dilaton of the transverse two dimensions. We argue that in some circumstances six-dimensional supersymmetry might help suppress quantum corrections to this cancellation down to the bulk supersymmetry-breaking scale, which is of order 1/r. We finally examine an explicit realization of the mechanism, in which 3-branes are inserted into an anomaly-free version of Salam-Sezgin gauged 6D supergravity compactified on a 2-sphere with nonzero magnetic flux. This realization is only partially successful due to a topological constraint which relates bulk couplings to the brane tension, although we give arguments why these relations may be stable against quantum corrections.