Compactifications of the Type II Superstring with D-branes and Fluxes
Type II compactifications with D-branes and background fluxes are viable candidates to relate string theory to the physics we observe in four dimensions. For simple toroidal orbifold backgrounds the D-brane and orientifold sector can be described by an ex
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Compactifications of the Type II Superstring with D-branes and Fluxes
Abstract Type II compactifications with D-branes and background fluxes are viable candidates to relate string theory to the physics we observe in four dimensions. For simple toroidal orbifold backgrounds the D-brane and orientifold sector can be described by an exact CFT, but issues such as tadpole cancellation, the GreenSchwarz mechanism, determining the massless spectrum etc. arise in a broader context and can be discussed from the low-energy-effective action perspective. String compactifications with non-vanishing NS-NS and R-R p-form field strengths provide solutions to the moduli problem, as these background fluxes modify the string equations of motion at leading order so that its solutions generically generate a potential for the would-be moduli fields. Thus they receive a vacuum expectation value and a mass. Basic knowledge of N D 1 supersymmetry in four dimensions is assumed.
17.1 Brane Worlds and Fluxes In Chap. 15 we have discussed orientifold compactification on toroidal orbifold backgrounds. In order to cancel the tadpoles introduced by the orientifold planes, one had to introduce D-branes, generically intersecting D-branes. The localization of gauge fields on D-branes provides a concrete stringy realization of the so-called brane world scenario, in which the Standard Model fields are confined on lower dimensional branes whereas gravity propagates in all ten space-time directions (the so-called bulk). It is an immediate consequence of the Dirac-Born-Infeld action that, if the branes on which the gauge degrees of freedom propagate wrap compact cycles of the internal manifold and if they also fill out the four non-compact space-time directions, then the four-dimensional gauge couplings are determined by the volume of the wrapped cycles. The gravitational coupling, on the other hand, depends on the total volume of the six dimensional compact manifold. This allows for the possibility of having the string scale Ms parametrically smaller than the Planck scale MP .
R. Blumenhagen et al., Basic Concepts of String Theory, Theoretical and Mathematical Physics, DOI 10.1007/978-3-642-29497-6 17, © Springer-Verlag Berlin Heidelberg 2013
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17 Compactifications of the Type II Superstring with D-branes and Fluxes
To see this, we compactify the ten-dimensional type II superstring theory to four dimensions on a compact six dimensional manifold X with volume VX and consider a Dp-brane filling the flat four-dimensional Minkowski space-time and wrapping a .p 3/-dimensional cycle C of X of volume VC . By dimensional reduction of the Einstein-Hilbert and Dirac-Born-Infeld actions to four dimensions, one can compute the effective four-dimensional Planck mass and gauge coupling MP2
8 8VX 8Ms2 vX D D ; 2 2 gs2 4 10 1
2 gYM
VC vC D : 2 2gs gDp
(17.1)
p3
are the dimensionless volumes vX D VX =`6s and vC D VC =`s p of X and of the wrapped cycle C in string units (recall from (2.12), `s D 2 ˛ 0 ). Note that the two couplings scale
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