arXiv subjects

Stefan Groot Nibbelink

Publications and source records attributed to Stefan Groot Nibbelink.

49 records · Page 3Linked to original sources

arXiv2006

Heterotic SO(32) model building in four dimensions

Four dimensional heterotic SO(32) orbifold models are classified systematically with model building applications in mind. We obtain all Z3, Z7 and Z2N models based on vectorial gauge shifts. The resulting gauge groups are reminiscent of those of type-I model building, as they always take the form SO(2n_0)xU(n_1)x...xU(n_{N-1})xSO(2n_N). The complete twisted spectrum is determined simultaneously for all orbifold models in a parametric way depending on n_0,...,n_N, rather than on a model by model basis. This reveals interesting patterns in the twisted states: They are always built out of vectors and anti--symmetric tensors of the U(n) groups, and either vectors or spinors of the SO(2n) groups. Our results may shed additional light on the S-duality between heterotic and type-I strings in four dimensions. As a spin-off we obtain an SO(10) GUT model with four generations from the Z4 orbifold.

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arXiv2006

Quantum Corrections to Non-Abelian SUSY Theories on Orbifolds

We consider supersymmetric non-Abelian gauge theories coupled to hyper multiplets on five and six dimensional orbifolds, S^1/Z_2 and T^2/Z_N, respectively. We compute the bulk and local fixed point renormalizations of the gauge couplings. To this end we extend supergraph techniques to these orbifolds by defining orbifold compatible delta functions. We develop their properties in detail. To cancel the bulk one-loop divergences the bulk gauge kinetic terms and dimension six higher derivative operators are required. The gauge couplings renormalize at the Z_N fixed points due to vector multiplet self interactions; the hyper multiplet renormalizes only non-Z_2 fixed points. In 6D the Wess-Zumino-Witten term and a higher derivative analogue have to renormalize in the bulk as well to preserve 6D gauge invariance.

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arXiv2005

Lorentz Violating Supersymmetric Quantum Electrodynamics

Theory of Supersymmetric Quantum Electrodynamics is extended by interactions with external vector and tensor backgrounds, that are assumed to be generated by some Lorentz-violating (LV) dynamics at an ultraviolet scale perhaps related to the Planck scale. Exact supersymmetry requires that such interactions correspond to LV operators of dimension five or higher, providing a solution to the naturalness problem in the LV sector. We classify all dimension five and six LV operators, analyze their properties at the quantum level and describe observational consequences of LV in this theory. We show that LV operators do not induce destabilizing D-terms, gauge anomaly and the Chern-Simons term for photons. We calculate the renormalization group evolution of dimension five LV operators and their mixing with dimension three LV operators, controlled by the scale of the soft-breaking masses. Dimension five LV operators are constrained by the low-energy precision measurements at 10^{-10}-10^{-5} level in units of the inverse Planck scale, while the Planck-scale suppressed dimension six LV operators are allowed by observational data.

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arXiv2005

Renormalization of Supersymmetric Gauge Theories on Orbifolds: Brane Gauge Couplings and Higher Derivative Operators

We consider supersymmetric gauge theories coupled to hyper multiplets on five and six dimensional orbifolds and determine the bulk and local fixed point renormalizations of the gauge couplings. We infer from a component analysis that the hyper multiplet does not induce renormalization of the brane gauge couplings on the five dimensional orbifold S^1/Z_2. This is not due to supersymmetry, since the bosonic and fermionic contributions cancel separately. We extend this investigation to T^2/Z_N orbifolds using supergraph techniques in six dimensions. On general Z_N orbifolds the gauge couplings do renormalize at the fixed points, except for the Z_2 fixed points of an even ordered orbifold. To cancel the bulk one-loop divergences a dimension six higher derivative operator is needed, in addition to the standard bulk gauge kinetic term.

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arXiv2005

Chiral gravity as a covariant formulation of massive gravity

We present a covariant nonlinear completion of the Fierz-Pauli (FP) mass term for the graviton. The starting observation is that the FP mass is immediately obtained by expanding the cosmological constant term, i.e. the determinant of the vielbein, around Minkowski space to second order in the vielbein perturbations. Since this is an unstable expansion in the standard case, we consider an extended theory of gravity which describes two vielbeins that give rise to chiral spin--connections (consequently, fermions of a definite chirality only couple to one of the gravitational sectors). As for Einstein gravity with a cosmological constant, a single fine-tuning is needed to recover a Minkowski background; the two sectors then differ only by a constant conformal factor. The spectrum of this theory consists of a massless and a massive graviton, with FP mass term. The theory possesses interesting limits in which only the massive graviton is coupled to matter at the linearized level.

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arXiv2005

Lorentz Violation in Supersymmetric Field Theories

We construct supersymmetric Lorentz violating operators for matter and gauge fields. We show that in the supersymmetric Standard Model the lowest possible dimension for such operators is five, and therefore they are suppressed by at least one power of an ultra--violet energy scale, providing a possible explanation for the smallness of Lorentz violation and its stability against radiative corrections. Supersymmetric Lorentz noninvariant operators do not lead to modifications of dispersion relations at high energies thereby escaping constraints from astrophysical searches for Lorentz violation.

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arXiv2004

Shape of gauge field tadpoles in string theory

Orbifolds in field theory are potentially singular objects for at their fixed points the curvature becomes infinite, therefore one may wonder whether field theory calculations near orbifold singularities can be trusted. String theory is perfectly well defined on orbifolds and can therefore be taken as a UV completion of field theory on orbifolds. We investigate the properties of field and string theory near orbifold singularities by reviewing the computation of a one loop gauge field tadpole. We find that in string theory the twisted states give contributions that have a spread of a couple of string lengths around the singularity, but otherwise the field theory picture is confirmed. One additional surprise is that in some orbifold models one can identify local tachyons that give contributions near the orbifold fixed point.

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arXiv2004

Vector/tensor duality in the five dimensional supersymmetric Green-Schwarz mechanism

The five dimensional version of the Green-Schwarz mechanism can be invoked to cancel U(1) anomalies on the boundaries of brane world models. In five dimensions there are two dual descriptions that employ either a two-form tensor field or a vector field. We present the supersymmetric extensions of these dual theories using four dimensional N=1 superspace. For the supersymmetrization of the five dimensional Chern-Simons three form this requires the introduction of a new chiral Chern-Simons multiplet. We derive the supersymmetric vector/tensor duality relations and show that not only is the usual one/two-form duality modified, but that there is also an interesting duality relation between the scalar components. Furthermore, the vector formulation always contains singular boundary mass terms which are absent in the tensor formulation. This apparent inconsistency is resolved by showing that in either formulation the four dimensional anomalous U(1) mass spectrum is identical, with the lowest lying Kaluza-Klein mode generically obtaining a finite nonzero mass.

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arXiv2003

Stringy profiles of gauge field tadpoles near orbifold singularities: I. heterotic string calculations

Closed string theories on orbifolds contain both untwisted and twisted states. The latter are normally assumed to live exactly at the orbifold fixed points. We perform a calculation of a gauge field tadpole amplitude and show that off-shell both the twisted and untwisted states give rise to non-trivial momentum profiles over the orbifold C^3/Z_3. These profiles take the form of Gaussian distributions integrated over the fundamental domain of the modular parameter of the torus. The propagators of the internal coordinate fields on the torus world sheet determine the width of the Gaussian profiles. These propagators are determined up to a single normal ordering constant which must be bounded below to allow the existence of the coordinate space representation of these Gaussians. Apart from the expected massless states, massive and even tachyonic string excitations contribute to the profiles in some anomalous U(1) models. However, when a tadpole is integrated over the internal dimensions, these tachyonic contributions cancel in a non-trivial manner.

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arXiv2003

Stringy profiles of gauge field tadpoles near orbifold singularities: II. field theoretical implications

Recent work has provided a direct string calculation of the internal coordinate dependence of gauge field tadpoles on the orbifold C^3/Z_3. We investigate the structure of these profiles in momentum and coordinate space representations using both analytical and numerical methods. The twisted states are determined to be localized within a few string lengths of the singularity. This provides an example of how delta-like singularities, which are typical for field theories on orbifolds, are avoided in string theory. A systematic expansion of the full string result allows us to speculate on how the leading stringy effects can be incorporated in a field theoretical description. In one heterotic model, we find that even though tachyons are not present in the physical spectrum, they totally dominate the tadpole profile in the vicinity of the fixed point.

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arXiv2003

Localization of heterotic anomalies on various hyper surfaces of T^6/Z_4

We investigate the structure of local anomalies of heterotic E_8 x E_8' theory on T^6/Z_4. We show that the untwisted states lead to anomalies in ten, six and four dimensions. At each of the six dimensional fixed spaces of this orbifold the twisted states ensure, that the anomalies factorize separately. As some of these twisted states live on T^2/Z_2, they give rise to four dimensional anomalies as well. At all four dimensional fixed points at worst a single Abelian anomaly can arise. Since the anomalies in all these dimensions factorize in a universal way, they can be canceled simultaneously. In addition, we show that for all U(1) factors at the four dimensional fixed points at least logarithmically divergent Fayet--Ilopoulos tadpoles are generated.

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arXiv2003

Cosmological bounds on large extra dimensions from non-thermal production of Kaluza-Klein modes

The existing cosmological constraints on theories with large extra dimensions rely on the thermal production of the Kaluza-Klein modes of gravitons and radions in the early Universe. Successful inflation and reheating, as well as baryogenesis, typically requires the existence of a TeV-scale field in the bulk, most notably the inflaton. The non-thermal production of KK modes with masses of order 100 GeV accompanying the inflaton decay sets the lower bounds on the fundamental scale M_*. For a 1 TeV inflaton, the late decay of these modes distort the successful predictions of Big Bang Nucleosynthesis unless M_*> 35, 13, 7, 5 and 3 TeV for 2, 3, 4, 5 and 6 extra dimensions, respectively. This improves the existing bounds from cosmology on M_* for 4, 5 and 6 extra dimensions. Even more stringent bounds are derived for a heavier inflaton.

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arXiv1998

Renormalization of the Electroweak Standard Model

These lecture notes give an introduction to the algebraic renormalization of the Standard Model. We start with the construction of the tree approximation and give the classical action and its defining symmetries in functional form. These are the Slavnov-Taylor identity, Ward identities of rigid symmetry and the abelian local Ward identity. The abelian Ward identity ensures coupling of the electromagnetic current in higher orders of perturbation theory, and is the functional form of the Gell-Mann-Nishijima relation. In the second part of the lectures we present in simple examples the basic properties of renormalized perturbation theory: scheme dependence of counterterms and the quantum action principle. Together with an algebraic characterization of the defining symmetry transformations they are the ingredients for a scheme independent unique construction of Green's functions to all orders of perturbation theory.

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