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

TL;DR

The paper argues that a six-dimensional supergravity framework with two large extra dimensions and branes can address both the high energy and low energy facets of the cosmological constant problem. It identifies a classical self tuning mechanism where brane tensions are automatically canceled by the bulk curvature and dilaton in 6D, yielding a vanishing 4D cosmological constant under suitable couplings. It further suggests that bulk supersymmetry suppresses quantum corrections to the cosmological constant to the order of $1/r^4$, aligning with the observed dark energy scale, though explicit quantum calculations are deferred. An explicit rugby ball compactification with magnetic flux demonstrates a topological constraint that ties bulk flux to brane tensions, offering stability considerations for the mechanism and motivating potential experimental probes in sub-millimeter gravity tests and collider physics.

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.