[Paper Review] Technically Natural Cosmological Constant From Supersymmetric 6D Brane Backreaction

C. P. Burgess, Leo van Nierop|arXiv (Cornell University)|Aug 1, 2011

Black Holes and Theoretical Physics4 citations

TL;DR

This paper proposes a 6D brane-world model where supersymmetry in the bulk stabilizes the Kaluza-Klein (KK) scale and cancels quantum corrections to the 4D cosmological constant. By coupling a non-supersymmetric 3-brane to a flux-stabilized 6D supergravity bulk, the model ensures flat 4D geometry via brane back-reaction, with quantum corrections generating a curvature of order $ m_{\text{KK}}^4 / M_p^2 $, naturally explaining the small observed dark energy scale without fine-tuning.

ABSTRACT

We provide an explicit example of a higher-dimensional model describing a non-supersymmetric spectrum of 4D particles of mass M, whose 4D geometry -- {\em including loop effects} -- has a curvature that is of order R ~ m_KK^4/M_p^2, where m_KK is the extra-dimensional Kaluza-Klein scale and M_p is the 4D Planck constant. m_KK is stabilized and can in particular satisfy m_KK << M. The system consists of a (5+1)-dimensional model with a flux-stabilized supersymmetric bulk coupled to non-supersymmetric matter localized on a (3+1)-dimensional positive-tension brane. We use recent techniques for calculating how extra dimensions respond to changes in brane properties to show (at the classical level) that the low-energy 4D geometry is exactly flat, independent of the value of the brane tensions. Its mechanism for doing so is the transfer of stabilizing flux between the bulk and the branes. The UV completion of the model can arise at scales much larger than M, allowing the calculation of quantum effects like the zero-point energy of very massive particles in the vacuum. We find that brane-localized loops do not affect the 4D curvature at all, but bulk loops can. These can be estimated on general grounds and we show that supersymmetry dictates that they generate curvatures that are generically of order m_KK^4/M_p^2. For realistic applications this points to a world with two supersymmetric extra dimensions, with supersymmetry in the bulk broken at the sub-eV KK scale - as proposed in hep-th/0304256 - requiring a 6D gravity scale somewhat higher than 10 TeV. Ordinary Standard Model particles are brane-localized and not at all supersymmetric (implying in particular no superpartners or the MSSM). We discuss how the model evades various no-go theorems that would naively exclude it, and briefly outline several striking observational implications for tests of gravity and at the LHC.

Motivation & Objective

• To resolve the cosmological constant problem by constructing a higher-dimensional model where the 4D vacuum energy does not gravitate strongly despite large quantum contributions.
• To show that a non-supersymmetric 4D spectrum can coexist with a flat 4D geometry due to extra-dimensional back-reaction effects.
• To demonstrate that quantum corrections from bulk loops — suppressed by supersymmetry — generate a curvature of order $ m_{\text{KK}}^4 / M_p^2 $, matching the observed dark energy scale.
• To evade no-go theorems that would otherwise forbid such a mechanism by ensuring brane-localized loops do not affect curvature.
• To establish a framework where the KK scale is stabilized at sub-eV energies, consistent with dark energy observations, via flux transfer between bulk and brane.

Proposed method

• Utilizes a (5+1)-dimensional supergravity bulk with flux compactification to classically stabilize the extra dimensions, preserving a single flat direction.
• Introduces a codimension-two 3-brane with positive tension and non-supersymmetric matter, coupled to the bulk via a Maxwell-like gauge field that allows flux transfer.
• Imposes two key conditions: no direct coupling to the bulk dilaton (scalar superpartner of the graviton), and a brane-localized flux that can absorb or emit bulk flux.
• Applies classical back-reaction techniques to show that the brane adjusts the extra-dimensional volume such that 4D geometry remains exactly flat regardless of brane tension.
• Analyzes quantum corrections using effective field theory, showing that bulk loops generate curvature $ \sim m_{\text{KK}}^4 / M_p^2 $, while brane-localized loops contribute zero net curvature.
• Relies on scale invariance and supersymmetry in the bulk to suppress quantum corrections, ensuring the final curvature is technically natural.

Experimental results

Research questions

• RQ1 Can a non-supersymmetric 4D particle spectrum coexist with a flat 4D geometry in a higher-dimensional theory?
• RQ2 How can the cosmological constant be naturally small in a 6D brane-world model with large vacuum energy on the brane?
• RQ3 What role does brane back-reaction play in stabilizing the extra dimensions and canceling curvature contributions?
• RQ4 Why do brane-localized quantum loops not contribute to the 4D curvature, while bulk loops do?
• RQ5 Can a 4D observer understand the mechanism without reference to extra dimensions, or is the 6D framework essential?

Key findings

• The model achieves a flat 4D geometry at the classical level due to back-reaction of the brane on the bulk, independent of brane tension.
• Quantum corrections from bulk loops generate a curvature of order $ m_{\text{KK}}^4 / M_p^2 $, which matches the observed dark energy density when $ m_{\text{KK}} \sim 10^{-3} \text{eV} $.
• Brane-localized loops do not affect the 4D curvature due to the absence of direct coupling to the bulk dilaton, preserving flatness.
• The KK scale is stabilized at sub-eV energies via flux transfer between bulk and brane, with the mechanism robust under quantum corrections.
• Supersymmetry in the bulk suppresses quantum corrections, ensuring the final curvature is technically natural and not fine-tuned.
• The model evades standard no-go theorems by relying on higher-dimensional dynamics and scale invariance, making a 4D-only description inconsistent.