Kähler moduli stabilization from ten dimensions

Abstract

We describe the back-reaction of gaugino condensates in supersymmetric AdS 4 Type II String Theory compactifications with fluxes. We use generalized complex geometry to capture the modification of the ten-dimensional supersymmetry equations and show that the cosmological constant prevents the cycle wrapped by the branes with gaugino condensation from shrinking to zero size. Thus, unlike in ordinary geometric transitions in flat space, the volume of this cycle remains finite. For D7 branes with gaugino condensation, this gives a ten-dimensional account of Kähler moduli stabilization. Furthermore, by matching the ten-dimensional supergravity solutions near and far from the cycle wrapped by the D7 branes, we find a relation between the size of this cycle and the cosmological constant. This relation agrees with the supersymmetric AdS vacuum condition obtained by KKLT using effective field theory.

Vacua with Small Flux Superpotential

“…Furthermore, we use up the action of the algebraic torus on X and the freedom to rescale f to set ψ 0,2,3,4,5 = 1. Then, along a codimension-one locus in moduli space specified by 22) one finds that f = df = 0 at the following set of points in X,…”

Conifold Vacua with Small Flux Superpotential

“…Furthermore, we use up the action of the algebraic torus on X and the freedom to rescale f to set 0,2,3,4,5 = 1. Then, along a codimension-one locus in moduli space specified by 22) one finds that f = df = 0 at the following set of points in X,…”

“…Kachru, Kallosh, Linde, and Trivedi (KKLT) famously proposed that orientifold compactifications of type IIB string theory that contain specific 'components' in the right proportions will admit parametrically controlled de Sitter vacua. [1] These components -a small classical flux superpotential, [2][3][4][5] a warped throat region, [6][7][8][9][10][11] a potential for the Kähler moduli from Euclidean D3-branes or strong gauge dynamics, [12][13][14][15][16][17][18][19][20][21][22][23] and a supersymmetry-breaking sector from anti-D3-branes [24][25][26][27][28][29][30][31] -are by now rather well understood separately. A remaining challenge in the pursuit of explicit examples of KKLT de Sitter vacua is to exhibit Calabi-Yau orientifolds that contain all these components at once, through calculations in which corrections to the leading approximations are demonstrably well-controlled.…”

Small Flux Superpotentials for Type IIB Flux Vacua Close to a Conifold

“…Moreover, it has been questioned whether the 4D description of the KKLT AdS minimum does really uplift to a full 10D solution of string theory. [4][5][6][7][8][9][10][11][12][13] Another important point is whether the effective action that is presumed to describe the strongly warped regime is really under control. Based on earlier work, [14] this question has been addressed recently.…”