Claudio A. Scrucca

Electroweak symmetry breaking and fermion masses from extra dimensions

We study higher-dimensional non-supersymmetric orbifold models where the Higgs field is identified with some internal component of a gauge field. We address two important and related issues that constitute severe obstacles towards model building within this type of constructions: the possibilities of achieving satisfactory Yukawa couplings and Higgs potentials. We consider models where matter fermions are localized at the orbifold fixed-points and couple to additional heavy fermions in the bulk. When integrated out, the latter induce tree-level non-local Yukawa interactions and a quantum contribution to the Higgs potential that we explicitly evaluate and analyse. The general features of these highly constrained models are illustrated through a minimal but potentially realistic five-dimensional example. Finally, we discuss possible cures for the persisting difficulties in achieving acceptable top and Higgs masses. In particular, we consider in some detail the effects induced in these models by adding localized kinetic terms for gauge fields.

Locally stable non-supersymmetric Minkowski vacua in supergravity

We perform a general study about the existence of non-supersymmetric minima with vanishing cosmological constant in supergravity models involving only chiral superfields. We study the conditions under which the matrix of second derivatives of the scalar potential is positive definite. We show that there exist very simple and strong necessary conditions for stability that constrain the Kahler curvature and the ratios of the supersymmetry-breaking auxiliary fields defining the Goldstino direction. We then derive more explicitly the implications of these constraints in the case where the Kahler potential for the supersymmetry-breaking fields is separable into a sum of terms for each of the fields. We also discuss the implications of our general results on the dynamics of moduli fields arising in string compactifications and on the relative sizes of their auxiliary fields, which are relevant for the soft terms of matter fields. We finally comment on how the idea of uplifting a supersymmetric AdS vacuum fits into our general study.

Anomalous couplings for D-branes and O-planes

We study anomalous Wess-Zumino couplings of D-branes and O-planes in a general background and derive them from a direct string computation by factorizing in the RR channel various one-loop amplitudes, In particular, we find that Op-planes present gravitational anomalous couplings involving the Hirzebruch polynomial (L) over cap, similarly to the roof genus (A) over cap encoding Dp-brane anomalous couplings, We determine, in each case, the precise dependence of these couplings on the curvature of the tangent and normal bundles

Anomalies, Fayet-Iliopoulos terms, and the consistency of orbifold field theories

We study the consistency of orbifold field theories and clarify to what extent the condition of having an anomaly-free spectrum of zero-modes is sufficient t o guarantee it. Preservation of gauge invariance at the quantum level is possible, although at the price, in general, of introducing operators that break the 5d local parity. These operators are, however, perfectly consistent with the orbifold projection. We also clarify the relation between localized Fayet–Iliopoulos (FI) terms and anomalies. These terms can be consistently added, breaking neither local supersymmetry nor gauge symmetry. In the framework of supergravity the localized FI term arises as the boundary completion of a bulk interaction term: given the bulk Lagrangian the FI is fixed by gauge invariance.

Nonlocal symmetry breaking in Kaluza-Klein theories

Scherk-Schwarz gauge symmetry breaking of a D-dimensional field theory model compactified on a circle is analyzed. It is explicitly shown that forbidden couplings in the unbroken theory appear in the one-loop effective action only in a nonlocal way, implying that they are finite at all orders in perturbation theory. This result can be understood as a consequence of the local gauge symmetry, but it holds true also in the global limit.

Constraints on modular inflation in supergravity and string theory

We perform a general algebraic analysis on the possibility of realising slow-roll inflation in the moduli sector of string models. This problem turns out to be very closely related to the characterisation of models admitting metastable vacua with non-negative cosmological constant. In fact, we show that the condition for the existence of viable inflationary trajectories is a deformation of the condition for the existence of metastable de Sitter vacua. This condition depends on the ratio between the scale of inflation and the gravitino mass and becomes stronger as this parameter grows. After performing a general study within arbitrary supergravity models, we analyse the implications of our results in several examples. More concretely, in the case of heterotic and orientifold string compactifications on a Calabi-Yau in the large volume limit we show that there may exist fully viable models, allowing both for inflation and stabilisation. Additionally, we show that subleading corrections breaking the no-scale property shared by these models always allow for slow-roll inflation but with an inflationary scale suppressed with respect to the gravitino scale. A scale of inflation larger than the gravitino scale can also be achieved under more restrictive circumstances and only for certain types of compactifications.

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 /(Z2 × Z ′). 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 their implications for realistic supersymmetric models with a single Higgs hypermultiplet in the bulk, and possible cancellation mechanisms in non-minimal models.

Constraints for the existence of flat and stable non-supersymmetric vacua in supergravity

We further develop on the study of the conditions for the existence of locally stable non-supersymmetric vacua with vanishing cosmological constant in supergravity models involving only chiral super fields. Starting from the two necessary conditions for flatness and stability derived in a previous paper (which involve the Kahler metric and its Riemann tensor contracted with the supersymmetry breaking auxiliary fields) we show that the implications of these constraints can be worked out exactly not only for factorizable scalar manifolds, but also for symmetric coset manifolds. In both cases, the conditions imply a strong restriction on the Kahler geometry and constrain the vector of auxiliary fields de ning the Goldstino direction to lie in a certain cone. We then apply these results to the various homogeneous coset manifolds spanned by the moduli and untwisted matter fields arising in string compactications, and discuss their implications. Finally, we also discuss what can be said for completely arbitrary scalar manifolds, and derive in this more general case some explicit but weaker restrictions on the Kahler geometry.

Anomalies and inflow on D-branes and O-planes

Abstract We derive the general form of the anomaly for chiral spinors and self-dual antisymmetric tensors living on D-brane and O-plane intersections, using both path-integral and index theorem methods. We then show that the anomalous couplings to RR forms of D-branes and O-planes in a general background are precisely those required to cancel these anomalies through the inflow mechanism. This allows, for instance, for local anomaly cancellation in generic orientifold models, the relevant Green-Schwarz term being given by the sum of the anomalous couplings of all the D-branes and O-planes in the model.

Gauge-Higgs unification in orbifold models

Six-dimensional orbifold models where the Higgs field is identified with some internal component of a gauge field are considered. We classify all possible T-2/Z(N) orbifold constructions based on a SU(3) electroweak gauge symmetry. Depending on the orbifold twist, models with two, one or zero Higgs doublets can be obtained. Models with one Higgs doublet are particularly interesting, as they lead to a prediction for the Higgs mass that is twice the W boson mass at leading order: m(H) = 2 m(W). The electroweak scale is quadratically sensitive to the cut-off, but only through very specific localized operators. We study in detail the structure of these operators at one loop, and identify a class of models where they do not destabilize the electroweak scale at the leading order. This provides a very promising framework to construct realistic and predictive models of electroweak symmetry breaking.