Supersymmetry Breaking and α′-Corrections to Flux Induced Potentials

Abstract

We obtain the vacuum solutions for M-theory compactified on eight-manifolds with non-vanishing four-form flux by analyzing the scalar potential appearing in the threedimensional theory. Many of these vacua are not supersymmetric and yet have a vanishing three-dimensional cosmological constant. We show that in the context of Type IIB compactifications on Calabi-Yau threefolds with fluxes and external brane sources α ′corrections generate a correction to the supergravity potential proportional to the Euler number of the internal manifold which spoils the no-scale structure appearing in the classical potential. This indicates that α ′ -corrections may indeed lead to a stabilization of the radial modulus appearing in these compactifications. April 2002the results of [17] by determining the minima of the potential calculated in [21]. This analysis will also show that the non-supersymmetric vacua found in [17] are classically stable. Our second aim is to investigate the fate of the no-scale structure of the potential if one considers the effect of higher derivative corrections of string theory and M-theory.We confirm the expectation of [5] that the no-scale structure in Type IIB compactifications does not survive in the quantum theory once higher order α ′ -corrections are taken into account. In particular, this implies that breaking supersymmetry via a (0,3)-flux induces a non-vanishing potential. Due to the relationship between Type IIB compactifications with three-form flux and M-theory compactifications with four-form flux [19], [25] a similar result should be valid for the non-supersymmetric fluxes in M-theory [17], which also lead to a vanishing cosmological constant at leading order.This paper is organized as follows. In section 2 we rederive the results of [17] from the scalar potential derived in [21] and show that the non-supersymmetric vacua are classically stable. In section 3 we calculate higher order α ′3 -corrections to the scalar potential computed in [5]. We show that these corrections generate a scalar potential that depends on the Calabi-Yau volume and is proportional to the Euler number of the internal manifold.This spoils the no-scale structure of the classical scalar potential for manifolds with nonvanishing Euler number and suggests that further α ′ -corrections may lead to a stabilization of the radial modulus. Some of the technical details of the computation are relegated to an appendix. (Non)-Supersymmetric Solutions in M-theoryIn this section we derive the non-supersymmetric vacuum solutions with vanishing cosmological constant computed in [17] from the superpotentials found in [19] and [21].We use the notation and conventions of [21]. The Scalar PotentialThe scalar potential of M-theory compactified on a fourfold Y 4 to three dimensions ground fluxes is performed in [22], [23] while the potential for M-theory on G 2 -holonomy manifolds with fluxes has been computed in [24].

Poly-instanton inflation

“…The noscale structure can be broken both by α ′ and g s effects. The leading order O(α ′3 ) correction to the Kähler potential has been computed in [31] and takes the form: 6) where…”

Compactifications of heterotic theory on non-Kähler complex manifolds, I

“…We note that the metric of (2.7) implies the connection 25) where dz 3 is the standard holomorphic one-form along the fiber. This expression assumes the origin of the coordinates (z 1 , z 2 ) to be at one of the fixed points of an involution of T 1 × T 2 .…”

“…This superpotential gives rise to a potential for the moduli fields of the internal manifold. In the supergravity approximation we will basically follow a similar approach as in [25], for compactifications of M-theory on Calabi-Yau four-folds. Thus, instead of extracting the superpotential from the potential for the scalars, we will be considering the dimensional reduction of a term quadratic in the gravitino appearing in the ten-dimensional action of N = 1 supergravity coupled to Super-Yang Mills theory.…”

“…The scalars coming from the two form anti-symmetric tensor field and the gauge fields have become charged. Therefore, their kinetic terms are given by covariant derivatives, defined as 25) where A µ are the Kaluza-Klein gauge fields.…”

Calabi-Yau fourfolds with flux and supersymmetry breaking

“…In [15], conditions on the flux for preserving N = 2 supersymmetry were derived. In particular, only a primitive flux of type (2,2) preserves N = 2. It was argued in [12] that this condition can be encoded in two superpotentials, whereas it was shown in [18] that the potential resulting from a Kaluza-Klein reduction involves one superpotential and a further contribution expressed via a real function closely related to the proposed second superpotential of [12].…”