A self-tuning mechanism in (3 + p)d gravity-scalar theory

We present a new type of self-tuning mechanism for ($3+p$)d brane worldmodels in the framework of gravity-scalar theory. This new type of self-tuningmechanism exhibits a remarkable feature. In the limit $g_s \to 0$, $g_s$ beingthe string coupling, the geometry of bulk spacetime remains virtually unchangedby an introduction of the Standard Model(SM)-brane, and consequently it isvirtually unaffected by quantum fluctuations of SM fields with support on theSM-brane. Such a feature can be obtained by introducing Neveu-Schwarz(NS)-braneas a background brane on which our SM-brane is to be set. Indeed, fieldequations naturally suggest the existence of the background NS-brane. Among thegiven such models, of the most interest is the case with $\Lambda=0$, where$\Lambda$ represents the bulk cosmological constant. This model contains a pairof coincident branes (of the SM- and the NS-branes), one of which is acodimension-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 (anti) T-duals of each other, and one of them may beidentified as our SM-brane plus the background NS-brane. In the presence of thebackground NS-brane (and in the absence of $\Lambda$), the 2d transverse space$\Sigma_2$ becomes an orbifold $R_2 /Z_n$ with an appropriate deficit angle.But this is only possible if the ($3+p$)d Planck scale $M_{3+p}$ and the stringscale $M_s$($\equiv 1/\sqrt{\alpha^{\prime}}$) are of the same order, whichaccords with the hierarchy assumption \cite{1,2,3} that the electroweak scale$m_{EW}$ is the only short distance scale existing in nature