1. Basic setup The basic setup for any string theory is the gravitational action in 10 d , which can be reduced to an effective 4 d with a metric ansatz: where µ, ν runs for the non-compact space-time, 4 d , while m, n runs for the compact 6 d . Demanding that in 4 d we arrive at N = 1 SUSY, g$_{mn}$ is required to be Calabi Yau mani- fold [40–42], a Ricci-flat metric with SU (3) holonomy. The compactification scale of 6 d is given by; M$_{c}$ ≪ M$_{s}$ , where M$_{c}$ is the compactification scale and M$_{s}$ is the string scale. The gravitational part of the action is given by: where e 6 u is the six dimensional volume of the compact metric and where 2 κ 2 10 = (2 π ) $^{7}$α ′ 4 [42]). Eq. (466) does not give the usual Einstein-Hilbert term for g$_{µν}$ ; therefore, a following transformation; g$_{µν}$ = e 6 $^{u}$e − 2 $^{φ}$g$_{µν}$ , leads to decouple the dilaton and the overall volume of the compactification. The string coupling is determined by g$_{s}$ = e $^{φ}$. Then the effective action is the usual Note that now there can be a large hierarchy between 10d and 4d Planck constants, due to a large warp factor, ∝ e $^{A}$, see [895–898]. For the rest of the discussion, an important ingredient will be the 10 d type IIB SUGRA, which arises as a low energy limit of type IIB string theory. The fields of IIB SUGRA are the metric, a complex scalar, two 3-form field strengths, and a self-dual 5-form field strength. The dilaton-axion scalar, τ = C$_{0}$ + ie − $^{φ}$, combines the RR scalar with the string coupling. It is convenient to combine the R-R ( F$_{3}$ = dC$_{2}$ ) and NS-NS ( H$_{3}$ = dB$_{2}$ ) 3-forms into a single complex field, F$_{3}$ = F$_{3}$ − CH$_{3}$ . The 5-form, ˜ F$_{5}$ = dC$_{4}$ − C$_{2}$H$_{3}$ , is neutral under self-duality, ⋆ ˜ F$_{5}$ = ˜ F$_{5}$ , which is imposed as an equation of motion [42], for a review see [44, 898]. There are other non-perturbative stringy objects such as D branes, a Dp brane is an extended hypersurface over p flat spatial dimensions in p + 1 dimensional space-time, where open strings are free to move [866, 867]. Open strings do not propagate in the bulk, while the 225 ds 2 = e 2 A ( x $^{$^{m}$)}$η$_{muν}$ dx $^{µ}$dxν + g$_{mn}$dx $^{m}$dx$^{n}$, (465) S = 1 2 κ 2 10 ∫ d 10 $_{x}$√ − g$_{10}$$_{e}$− 2 $^{φ}$R$_{10}$ = 1 2 κ 2 10 ∫ d 10 $_{x}$√ − g$_{4}$e 2 $^{A}$e 6 u $_{e}$− 2 $^{φ}$R$_{4}$ (466) S = 1 2 κ 2 4 ∫ d 4 $_{x}$√ − g$_{E}$R$_{E}$ , 1 κ 2 4 = V$_{6}$ κ 2 10 , V$_{6}$ = ∫ d $^{6}$x √ det g$_{mn}$ e 2 A $_{e}$− 6 u . (467)