Warped Kähler potentials and fluxes

Abstract

The four-dimensional effective theory for type IIB warped flux compactifications proposed in [1] is completed by taking into account the backreaction of the Kähler moduli on the three-form fluxes. The only required modification consists in a fluxdependent contribution to the chiral fields parametrising the Kähler moduli. The resulting supersymmetric effective theory satisfies the no-scale condition and consistently combines previous partial results present in the literature. Similar results hold for M-theory warped compactifications on Calabi-Yau fourfolds, whose effective field theory and Kähler potential are also discussed.

Dimensional reduction for D3-brane moduli

“…and corrected by flux dependence on metric moduli [19]; the contribution from the flux background to C IJ already appeared in direct dimensional reduction in [26]. In the case that the CY metricg mn is formal or that we restrict to the universal axion (ω 2 =J 2 , the almost complex structure), C IJ = e 2Ω δ IJ .…”

“…One challenge for the construction of an effective theory in GKP backgrounds is that the metric becomes a warped product between the internal and external spaces, complicating the identification of the degrees of freedom. The supersymmetry of the background along with the fact that scaling the warp factor can be removed with a 10D diffeomorphism has allowed [16][17][18][19] to derive many aspects of the effective theory without a direct dimensional reduction.…”

“…The internal component (C. 19) is once again a dynamical EOM only, and we can simplify it to the form (4.44) using (3.22).…”

Type IIA flux vacua and α′-corrections

“…and the lower order curvature corrections K Next, we evaluate the expression of the scalar potential (A.17) for this flux background and use the Hodge duality relations for the harmonic three-forms (A. 19), such that a bilinear structure in terms of the axion polynomials emerges explicitly. After the appropriate Weyl rescaling to 4d Einstein frame we obtain which equally allows to switch between the flux quanta basis (e 0 , e a , −m, m a ) and (e 0 , e a , m a , m).…”

The cosmological constant and the electroweak scale

“…While the brane positions are good Kähler moduli for the effective field theory, the presence of D3-branes leads a redefinition of both the Kähler coordinate T and the term K K in the Kähler potential (2.1). Using Φ i = Z i /2πα and setting momentarily ξ = 0, we have [22][23][24]…”