An effective description of the landscape — I

Abstract

We study under what conditions massive fields can be "frozen" rather than integrated out in certain four dimensional theories with global or local N = 1 supersymmetry. We focus on models without gauge fields, admitting a superpotential of the form W = W 0 (H) + ǫ W 1 (H, L), with ǫ ≪ 1, where H and L schematically denote the heavy and light chiral superfields. We find that the fields H can always be frozen to constant values H 0 , if they approximately correspond to supersymmetric solutions along the H directions, independently of the form of the Kähler potential K for H and L, provided K is sufficiently regular. In supergravity W 0 is required to be of order ǫ at the vacuum to ensure a mass hierarchy between H and L. The backreaction induced by the breaking of supersymmetry on the heavy fields is always negligible, leading to suppressed F H -terms. For factorizable Kähler potentials W 0 can instead be generic. Our results imply that the common way complex structure and dilaton moduli are stabilized, as in Phys. Rev. D 68 (2003) 046005 by Kachru et al., for instance, is reliable to a very good accuracy, provided W 0 is small enough.

Universal properties of type IIB and F-theory flux compactifications at large complex structure

“…Including such interactions will generically affect the spectra, unless the additional sectors can be integrated out or consistently truncated while preserving supersymmetry [19][20][21][22][23][24][25]. In string compactifications, the form of the interactions with the Kähler sector is partly determined by the corresponding moduli stabilisation mechanism, which we here don't specify.…”

SUSY breaking in local string/F-theory models

“…scalar potential is at order O(V −3 ) in the LARGE volume expansion and that the Kähler metric for the complex structure and Kähler moduli has a factorised form (for discussions of integrating out moduli in supergravity see [28][29][30][31]). Working in the large cycle regime, in the simplest case, one chooses the volume V of the internal space to be of swiss-cheese form with three Kähler moduli…”

A note on the magnitude of the flux superpotential

“…Using −ĝ (10) = −g (4) √ g (6) ω 2 e −6u and d 6 y ∝ M −6 s , expanding the action in powers of fluctuations and focussing on the four-dimensional scalar KK modes ϕ i contained within h mn , gives the following four-dimensional Einstein term and scalar kinetic terms:…”

“…In order to trust the four-dimensional effective field theory, one has to check that the effects used to fix the Kähler moduli, develop a potential whose VEV satisfies V ≪ M 4 KK . For a systematic treatment of integrating out of the complex structure and dilaton see [5][6][7].…”