A self-tuning mechanism in 6d gravity-scalar theory

Abstract

We present a new type of self-tuning mechanism for 6d brane world models in the framework of gravity-scalar theory. This new type of self-tuning mechanism exhibits a remarkable feature. In the weak coupling limit $g_s \to 0$, the geometry of bulk spacetime remains virtually unchanged by an introduction of the Standard Model(SM)-brane, and consequently it is virtually unaffected by quantum corrections to the brane tension due to the dynamics of SM degrees of freedom. Such a feature can be obtained by introducing Neveu-Schwarz(NS)-brane as a background brane on which our SM-brane is to be set. Indeed, field equations naturally require the existence of the background NS-brane. Among the given such models, of the most interest is the case with $\Lambda=0$, where $\Lambda$ represents the bulk cosmological constant. This model contains two coincident branes (of the SM- and the NS-branes), one of which is a codimension-2 brane placed at the origin of 2d transverse space ($\equiv \Sigma_2$), another a codimension-1 brane placed at the edge of $\Sigma_2$. These two branes are T-duals of each other, and one of them is identified as our SM-brane (plus the background NS-brane). In the presence of the background NS-brane (and in the absence of $\Lambda$), the 2d transverse space $\Sigma_2$ becomes $R_2$ (or an orbifold $R_2 /Z_n$) with an appropriate deficit angle. But this is possible only if the 6d Planck scale $M_6$ and the string scale $M_s$($\equiv 1/\sqrt{\alpha^{\prime}}$) are of the same order, which accords with an assumption \cite{1,2,3} that the electroweak scale $m_{EW}$ is the only short distance scale in nature