Gaugino Condensation and Nonperturbative Superpotentials in Flux Compactifications

By Lars Goerlich, S. Kachru, P. Tripathy, S. Trivedi. 2004

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Department of Physics and SLACStanford UniversityStanford, CA 94305/94309, USAThere are two known sources of nonperturbative superpotentials for Kahler moduli intype IIB orientifolds, or F-theory compactiﬁcations on Calabi-Yau fourfolds, with ﬂux:Euclidean brane instantons and low-energy dynamics in D7 brane gauge theories. The ﬁrstclass of eﬀects, Euclidean D3 branes which lift in M-theory to M5 branes wrapping divisorsof arithmetic genus 1 in the fourfold, is relatively well understood. The second class hasbeen less explored. In this paper, we consider the explicit example of F-theory on K3×K3with ﬂux. The ﬂuxes lift the D7 brane matter ﬁelds, and stabilize stacks of D7 branes atloci of enhanced gauge symmetry. The resulting theories exhibit gaugino condensation,and generate a nonperturbative superpotential for Kahler moduli. We describe how therelevant geometries in general contain cycles of arithmetic genus χ ≥ 1 (and how χ > 1divisors can contribute to the superpotential, in the presence of ﬂux). This second class ofeﬀects is likely to be important in ﬁnding even larger classes of models where the KKLTmechanism of moduli stabilization can be realized. We also address various claims aboutthe situation for IIB models with a single Kahler modulus.July 2004

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/3686ec0ae47ad3a70fa0add0fb825409ca95d2d7

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Citations in the corpus

Large-volume flux compactifications: Moduli spectrum and D3/D7 soft supersymmetry breaking (2005, background): “The exact necessary conditions are not yet known, but the trend of recent results [33, 34, 35, 36, 37] is that the condition χ(D) = 1 will be substantially relaxed.”
d-Brane Instantons in Type II Orientifolds (2009, background): “Most efforts in the literature have focused on the flux-induced lifting of deformation zero modes of M5-brane instantons in M/F-theory [92, 93, 94, 95] and of E3-brane instantons in Type IIB orientifolds [96, 97, 98, 99, 100, 101, 102].”
Lectures on F-theory compactifications and model building (2010, background): “Various aspects of (flux) potentials in F-theory on K3×K3 have been analysed in [61–67].”
Les Houches Lectures on Constructing String Vacua (2008, background): “More discussion of this issue and more concrete examples of flux modifications of M5 instanton effects can be found in [94–98].”
Building MSSM flux vacua (2004, result): “These effects imply that ISD fluxes not only stabilise closed string moduli, but can also give masses to open string moduli, in agreement with the results in [50, 51].”
D-terms and F-terms from D7-brane fluxes (2005, background): “The German Science Foundation, European RTN Program MRTN-CT2004-503369 and the DAAD – the German Academic Exchange Service.”
Dynamics of warped compactifications and the shape of the warped landscape (2005, background): “Consequently for some values of the parameters, the potential can produce a minimum at positive vacuum energy.”
TOWARD REALISTIC INTERSECTING D-BRANE MODELS (2005, background): “For the same reason that soft terms are generated, the background flux can also induce a mass to some of the open string moduli and thus provide a way to stabilize them [171, 172, 153].”
The effective action of D7-branes in N=1 Calabi-Yau orientifolds (2004, unknown): “For example, gaugino condensation on hidden D7-branes and/or Euclidean D3-brane instantons have been suggested as additional non-perturbative contributions to the potential [35] [36] [37].”
Fixing all moduli in a simple f-theory compactification (2005, background): “8 In certain circumstances, divisors of χh > 1 can contribute [53,66,98].”