Eun Kyung Park, Pyung Seong Kwon
We propose a new type of self-tuning mechanism to address the cosmological constant problem, based on the viewpoint that our three-dimensional space is a stack of the BPS D3-branes located at the conifold singularity of the Calabi-Yau three-fold. In this self-tuning mechanism the four-dimensional cosmological constant $\lambda$ appears as a sum of two types, NS-NS type and R-R type, of vacuum energies on the brane and these two types of vacuum energies are forced to cancel by field equations so that $\lambda$ tunes itself to zero as a result. Also in this self-tuning mechanism the $d=4$ supersymmetry is broken in the brane region, while maintaining $\lambda =0$ in both the brane and bulk regions. The supersymmetry breaking occurs as a result of the gauge symmetry breaking of the R-R four-form arising at the quantum level. So the brane region is locally anomalous. But the total anomaly of the brane region vanishes by the self-tuning condition $\lambda=0$. The substance of the supersymmetry breaking term of the action is a vacuum energy density (on the brane) arising from the quantum excitations with components along the transverse directions to the D3-brane. The supersymmetry breaking gives a mass to the dilaton which is estimated to be $m_{\Phi}^2 \sim g_s m_s^2$ where $m_s$ is the string mass scale, $m_s \equiv 1/\sqrt{\alpha^{\prime}}$. Using $m_{\Phi} \approx m_{\rm sp}$, where $m_{\rm sp}$ being the typical mass scale of the Standard Model superpartners, we obtain $m_{\rm sp}^2 \sim g_s m_s^2$. It is finally argued that the configuration with broken supersymmetry is more favored by the action principle than the other with unbroken supersymmetry.
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http://arxiv.org/abs/1301.1783
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