Kahler Anomalies in Supergravity and Flux Vacua

We review the subject of Kahler anomalies in gauged supergravity, emphasizing that field equations are inconsistent when the Kahler potential is non-invariant under gauge transformations or when there are elementary Fayet-Iliopoulos couplings. Flux vacua solutions of string theory with gauged U(1) shift symmetries appear to avoid this problem. The covariant Kahler anomalies involve tensors which are composite functions of the scalars as well as the gauge field strength and space-time curvature tensors. Anomaly cancellation conditions will be discussed in a sequel to this paper.Comment: 29 pages; v2: revised presentation, section on Fayet-Iliopoulos couplings cut, effects of gauginos on anomalies included, references adde

D-type supersymmetry breaking and brane-to-brane gravity mediation

We revisit the issue of gravitational contributions to soft masses in five-dimensional sequestered models. We point out that, unlike for the case of F-type supersymmetry breaking, for D-type breaking these effects generically give positive soft masses squared for the sfermions. This drastically improves model building. We discuss the phenomenological implications of our result.Comment: 16 pages. Typos corrected, minor clarifications. To be published in Phys. Lett.

Anomaly Cancellation in Supergravity with Fayet-Iliopoulos Couplings

We review and clarify the cancellation conditions for gauge anomalies which occur when N=1, D=4 supergravity is coupled to a Kahler non-linear sigma-model with gauged isometries and Fayet-Iliopoulos couplings. For a flat sigma-model target space and vanishing Fayet-Iliopoulos couplings, consistency requires just the conventional anomaly cancellation conditions. A consistent model with non-vanishing Fayet-Iliopoulos couplings is unlikely unless the Green-Schwarz mechanism is used. In this case the U(1) gauge boson becomes massive and the D-term potential receives corrections. A Green-Schwarz mechanism can remove both the abelian and certain non-abelian anomalies in models with a gauge non-invariant Kahler potential.Comment: 27 page

Effective theoretical approach of Gauge-Higgs unification model and its phenomenological applications

We derive the low energy effective theory of Gauge-Higgs unification (GHU) models in the usual four dimensional framework. We find that the theories are described by only the zero-modes with a particular renormalization condition in which essential informations about GHU models are included. We call this condition ``Gauge-Higgs condition'' in this letter. In other wards, we can describe the low energy theory as the SM with this condition if GHU is a model as the UV completion of the Standard Model. This approach will be a powerful tool to construct realistic models for GHU and to investigate their low energy phenomena.Comment: 18 pages, 2 figures; Two paragraphs discussing the applicable scope of this approach are adde

Open string models with Scherk-Schwarz SUSY breaking and localized anomalies

We study examples of chiral four-dimensional IIB orientifolds with Scherk--Schwarz supersymmetry breaking, based on freely acting orbifolds. We construct a new Z3xZ3' model, containing only D9-branes, and rederive from a more geometric perspective the known Z6'xZ2' model, containing D9, D5 and \bar D 5 branes. The cancellation of anomalies in these models is then studied locally in the internal space. These are found to cancel through an interesting generalization of the Green--Schwarz mechanism involving twisted Ramond--Ramond axions and 4-forms. The effect of the latter amounts to local counterterms from a low-energy effective field theory point of view. We also point out that the number of spontaneously broken U(1) gauge fields is in general greater than what expected from a four-dimensional analysis of anomalies.Comment: v2: 28 pages, references added; v3: version to appear in Nucl.Phys.

Towards Z_2-protected gauge--Higgs unification

In theories with flux compactification in eight or higher dimensions, the extra-dimensional components of the gauge field may be regarded as the Higgs field candidates. We suggest a way to protect these components from getting large tree-level masses by imposing a $Z_2$-symmetry acting on compact manifolds and background fields on them. In our scheme the infinite series of heavy KK modes naturally decouples from the light Higgs candidates, whose number is generically larger than one. We also present toy models with three families of leptons, illustrating that the Yukawa sector in our scheme is fairly strongly constrained. In one of these models, one fermion gets a tree-level mass after electroweak symmetry breaking, while two others remain naturally massless at the tree level.Comment: A few points clarified. Journal versio

Minimal gauge-Higgs unification with a flavour symmetry

We show that a flavour symmetry a la Froggatt-Nielsen can be naturally incorporated in models with gauge-Higgs unification, by exploiting the heavy fermions that are anyhow needed to realize realistic Yukawa couplings. The case of the minimal five-dimensional model, in which the SU(2)_L x U(1)_Y electroweak group is enlarged to an SU(3)_W group, and then broken to U(1)_em by the combination of an orbifold projection and a Scherk-Schwarz twist, is studied in detail. We show that the minimal way of incorporating a U(1)_F flavour symmetry is to enlarge it to an SU(2)_F group, which is then completely broken by the same orbifold projection and Scherk-Schwarz twist. The general features of this construction, where ordinary fermions live on the branes defined by the orbifold fixed-points and messenger fermions live in the bulk, are compared to those of ordinary four-dimensional flavour models, and some explicit examples are constructed.Comment: LaTex, 37 pages, 2 figures; some clarifying comments and a few references adde

Anomalies in orbifold field theories

We study the constraints on models with extra dimensions arising from local anomaly cancellation. We consider a five-dimensional field theory with a U(1) gauge field and a charged fermion, compactified on the orbifold S^1/(Z_2 x Z_2'). We show that, even if the orbifold projections remove both fermionic zero modes, there are gauge anomalies localized at the fixed points. Anomalies naively cancel after integration over the fifth dimension, but gauge invariance is broken, spoiling the consistency of the theory. We discuss the implications for realistic supersymmetric models with a single Higgs hypermultiplet in the bulk, and possible cancellation mechanisms in non-minimal models.Comment: 10 pages, 2 figures, LaTex; v2: final version to be published in Phys. Lett.

Breaking the electroweak symmetry and supersymmetry by a compact extra dimension

We revisit in some more detail a recent specific proposal for the breaking of the electroweak symmetry and of supersymmetry by a compact extra dimension. Possible mass terms for the Higgs and the matter hypermultiplets are considered and their effects on the spectrum analyzed. Previous conclusions are reinforced and put on firmer ground.Comment: 25 pages, LaTeX, 9 eps figure