S. Groot Nibbelink

Scalar perturbations during multiple field slow-roll inflation

We calculate the scalar gravitational and matter perturbations in the context of slow-roll inflation with multiple scalar fields, that take values on a (curved) manifold, to first order in slow roll. For this purpose a basis for these perturbations determined by the background dynamics is introduced and multiple-field slow-roll functions are defined. To obtain analytical solutions to first order, the scalar perturbation modes have to be treated in three different regimes. Matching is performed by identifying leading order asymptotic expansions analytically in different regions. The possible sources for multiple-field effects in the gravitational potential are the particular solution caused by the coupling to the field perturbation perpendicular to the field velocity, and the rotation of the basis. The former can contribute even to leading order if the corresponding multiple-field slow-roll function is sizable during the last 60 e-folds. Making some simplifying assumptions, the evolution of adiabatic and isocurvature perturbations after inflation is discussed. The analytical results are illustrated and checked numerically with the example of a quadratic potential.

Gauge corrections and FI-term in 5D KK theories

Abstract In the context of a five-dimensional N =1 Kaluza–Klein model compactified on S 1 / Z 2 × Z 2 ′ we compute the one-loop gauge corrections to the self energy of the (zero-mode) scalar field. The result is quadratically divergent due to the appearance of a Fayet–Iliopoulos term.

Instabilities of bulk fields and anomalies on orbifolds

Abstract Bulk matter modes of higher-dimensional models generically become unstable in the presence of additional matter multiplets at the branes. This quantum instability is driven by localized Fayet–Iliopoulos terms that attract the bulk zero modes towards the boundary branes. We study this mechanism in the framework of a 5-dimensional S 1 / Z 2 orbifold and give conditions for the various possibilities of localization of (chiral) zero modes. This mechanism is quite relevant for realistic model building, as the standard model contains U(1) hypercharge with potentially localized FI-terms. The analysis is closely related to localized anomalies in higher-dimensional gauge theories. Five-dimensional gauge invariance of the effective action determines the anomaly constraints and fixes the normalization of Chern–Simons terms. The localization of the bulk modes does not effect the anomaly cancellation globally, but the additional heavy Kaluza–Klein modes of the bulk fields may cancel the Chern–Simons terms. We discuss also the potential appearance of the parity anomaly that might render the construction of some orbifold models inconsistent.

Spontaneous localization of bulk matter fields

Abstract We study models compactified on S 1 / Z 2 with bulk and brane matter fields charged under U (1) gauge symmetry. We calculate the FI-terms and show by minimizing the resulting potential that supersymmetry or gauge symmetry is spontaneously broken if the sum of the charges does not vanish. Even if this sum vanishes, there could be an instability as a consequence of localized FI-terms. This leads to a spontaneous localization of charged bulk fields on respective branes.

Localized anomalies in heterotic orbifolds

Abstract Recently spatially localized anomalies have been considered in higher-dimensional field theories. The question of the quantum consistency and stability of these theories needs further discussion. Here we would like to investigate what string theory might teach us about theories with localized anomalies. We consider the Z 3 orbifold of the heterotic E 8 ×E′ 8 theory, and compute the anomaly of the gaugino in the presence of Wilson lines. We find an anomaly localized at the fixed points, which depends crucially on the local untwisted spectra at those points. We show that non-Abelian anomalies cancel locally at the fixed points for all Z 3 models with or without additional Wilson lines. At various fixed points different anomalous U(1)s may be present, but at most one at a given fixed point. It is in general not possible to construct one generator which is the sole source of the anomalous U(1)s at the various fixed points.

String Threshold corrections from Field Theory

Abstract A field theory approach to summing threshold effects to the gauge couplings in a two-torus compactification is presented and the link with the (heterotic) string calculation is carefully investigated. We analyse whether the complete UV behaviour of the theory may be described on pure field theory grounds, as due to momentum modes only, and address the role of the winding modes, not included by the field theory approach. “Non-decoupling” effects in the low energy limit, due to a small dimension are discussed. The role of modular invariance in ensuring a finite (heterotic) string result is addressed.

Matter coupling and anomaly cancellation in supersymmetric sigma models

Generalized matter couplings to four-dimensional supersymmetric sigma models on gen- eral Kahler manifolds are presented, preserving all holomorphic symmetries. Our gen- eralization allows assignment of arbitrary U(1) charges to additional matter fermions, in all representations of (the holomorphic part of) the isometry group. This can be used to eliminate unwanted 5 anomalies, in particular for the U(1) symmetry arising from the complex structure of the target space. A consistent gauging of this isometry group, or any of its subgroups, then becomes possible. When gauged in the presence of a chiral scalar multiplet, the U(1) symmetry is broken spontaneously, generating a mass for the U(1) vector multiplet via the supersymmetric Higgs effect. As an example we discuss the case of the homogeneous coset space E6/SO(10) × U(1).

Construction and analysis of anomaly-free supersymmetric SO(2N)/U(N) σ-models

Abstract This paper discusses a procedure for the consistent coupling of gauge- and matter superfields to supersymmetric sigma-models on symmetric coset spaces of Kahler type. We exhibit the finite isometry transformations and the corresponding Kahler transformations. These lead to the construction of a generalized type of Killing potentials. In certain cases a charge quantization condition needs to be imposed to guarantee the global existence of a line bundle on a coset space. The results are applied to the explicit construction of sigma-models on cosets SO(2N)/U(N) . Only a finite number of these models can consistently incorporate matter in representations descending from the spinorial representations of SO(2N) . We investigate in detail some aspects of the vacuum structure of the gauged SO(10)/U(5) theory, with surprising results: the fully gauged minimal anomaly-free model is shown to be singular, as the kinetic terms of the quasi-Goldstone fermions vanish in the vacuum. Gauging only the linear isometry group SU(5)×U(1) , or one of its subgroups, can give a physically well-behaved theory. With gauged U(1) this requires the Fayet–Iliopoulos term to take values in a specific limited range.

Line bundles in supersymmetric coset models

Abstract The scalars of an N =1 supersymmetric σ -model in 4 dimensions parameterize a Kahler manifold. The transformations of their fermionic superpartners under the isometries are often anomalous. These anomalies can be canceled by introducing additional chiral multiplets with appropriate charges. To obtain the right charges a non-trivial singlet compensating multiplet can be used. However when the topology of the underlying Kahler manifold is non-trivial, the consistency of this multiplet requires that its charge is quantized. This singlet can be interpreted as a section of a line bundle. We determine the Kahler potentials corresponding to the minimal non-trivial singlet chiral superfields for any compact Kahlerian coset space G / H . The quantization condition may be in conflict with the requirement of anomaly cancelation. To illustrate this, we discuss the consistency of anomaly free models based on the coset spaces E 6 / SO (10)× U (1) and SU (5)/ SU (2)× U (1)× SU (3).