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S. Groot Nibbelink

Publications and source records attributed to S. Groot Nibbelink.

At least 19 recordsLinked to original sources
arXiv2022

The fate of discrete torsion on resolved heterotic Z2xZ2 orbifolds using (0,2) GLSMs

This paper aims to shed light on what becomes of discrete torsion within heterotic orbifolds when they are resolved to smooth geometries. Gauged Linear Sigma Models (GLSMs) possessing (0,2) worldsheet supersymmetry are employed as interpolations between them. This question is addressed for resolutions of the non-compact C3/Z2xZ2 and the compact T6/Z2xZ2 orbifolds to keep track of local and global aspects. The GLSMs associated with the non-compact orbifold with or without torsion are to a large extent equivalent: only when expressed in the same superfield basis, a field redefinition anomaly arises among them, which in the orbifold limit reproduces the discrete torsion phases. Previously unknown, novel resolution GLSMs for T6/Z2xZ2 are constructed. The GLSM associated with the torsional compact orbifold suffers from mixed gauge anomalies, which need to be cancelled by appropriate logarithmic superfield dependent FI-terms on the worldsheet, signalling H-flux due to NS5-branes supported at the exceptional cycles.

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arXiv2022

Taming Triangulation Dependence of T6/Z2xZ2 Resolutions

Resolutions of certain toroidal orbifolds, like T6/Z2xZ2, are far from unique, due to triangulation dependence of their resolved local singularities. This leads to an explosion of the number of topologically distinct smooth geometries associated to a single orbifold. By introducing a parameterisation to keep track of the triangulations used at all resolved singularities simultaneously, (self-)intersection numbers and integrated Chern classes can be determined for any triangulation configuration. Using this method the consistency conditions of line bundle models and the resulting chiral spectra can be worked out for any choice of triangulation. Moreover, by superimposing the Bianchi identities for all triangulation options much simpler though stronger conditions are uncovered. When these are satisfied, flop--transitions between all different triangulations are admissible. Various methods are exemplified by a number of concrete models on resolutions of the T6/Z2xZ2 orbifold.

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arXiv2021

Uncovering a Spinor-Vector Duality on a Resolved Orbifold

Spinor-vector dualities have been established in various exact string realisations like orbifold and free fermionic constructions. This paper aims to investigate possibility of having spinor-vector dualities on smooth geometries in the context of the heterotic string. As a concrete working example the resolution of the T4/Z2 orbifold is considered with an additional circle supporting a Wilson line, for which it is known that the underlying orbifold theory exhibits such a duality by switching on/off a generalised discrete torsion phase between the orbifold twist and the Wilson line. Depending on this phase complementary parts of the twisted sector orbifold states are projected out, so that different blowup modes are available to generate the resolutions. As a consequence, not only the spectra of the dual pairs are different, but also the gauge groups are not identical making this duality less apparent on the blowup and thus presumably on smooth geometries in general.

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arXiv2021

Constraint on Spinor-Vector Dualities in Six Dimensions

Imprints of spinor-vector dualities have been uncovered in various string constructions. They are typically induced by changing certain free general GSO phases in the underlying string partition functions. This paper shows that spinor-vector dualities in six dimensions are constrained by a fundamental effective field theory consistency condition, namely that any six dimensional low energy theory must be free of irreducible SO(2N) anomalies. Aspects of spinor-vector dualities are analysed in four six-dimensional free fermionic models which are distinguished by two generalised GSO phases. In addition, the constraint on the number of spinors and vectors is confirmed on generic spectra which may occur in K3 line bundle compactifications of the heterotic E8xE8 string.

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arXiv2016

Heterotic free fermionic and symmetric toroidal orbifold models

Free fermionic models and symmetric heterotic toroidal orbifolds both constitute exact backgrounds that can be used effectively for phenomenological explorations within string theory. Even though it is widely believed that for Z2xZ2 orbifolds the two descriptions should be equivalent, a detailed dictionary between both formulations is still lacking. This paper aims to fill this gap: We give a detailed account of how the input data of both descriptions can be related to each other. In particular, we show that the generalized GSO phases of the free fermionic model correspond to generalized torsion phases used in orbifold model building. We illustrate our translation methods by providing free fermionic realizations for all Z2xZ2 orbifold geometries in six dimensions.

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arXiv2007

Multiple anomalous U(1)s in heterotic blow-ups

The existence of multiple anomalous U(1)s is demonstrated explicitly in a blow-up version of a heterotic Z_3 orbifold. Another blow-up of the same orbifold supports further evidence for the type-I/heterotic duality in four dimensions. It has a single anomalous U(1) which does not factorize universally. As multiple anomalous U(1)s as well as non-universal factorization have never been established on heterotic orbifolds explicitely, these findings might appear contradictory at first sight. Possible inconsistencies are avoided by reinterpreting a charged twisted state as a second non-universal localized axion. The mismatch between the charges of the orbifold and blow-up spectra is resolved by suitable field redefinitions. The anomaly of the field redefinitions corresponds to the difference of blow-up and heterotic orbifold anomalies.

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arXiv2007

Resolutions of C^n/Z_n Orbifolds, their U(1) Bundles, and Applications to String Model Building

We describe blowups of C^n/Z_n orbifolds as complex line bundles over CP^{n-1}. We construct some gauge bundles on these resolutions. Apart from the standard embedding, we describe U(1) bundles and an SU(n-1) bundle. Both blowups and their gauge bundles are given explicitly. We investigate ten dimensional SO(32) super Yang-Mills theory coupled to supergravity on these backgrounds. The integrated Bianchi identity implies that there are only a finite number of U(1) bundle models. We describe how the orbifold gauge shift vector can be read off from the gauge background. In this way we can assert that in the blow down limit these models correspond to heterotic C^2/Z_2 and C^3/Z_3 orbifold models. (Only the Z_3 model with unbroken gauge group SO(32) cannot be reconstructed in blowup without torsion.) This is confirmed by computing the charged chiral spectra on the resolutions. The construction of these blowup models implies that the mismatch between type-I and heterotic models on T^6/Z_3 does not signal a complication of S-duality, but rather a problem of type-I model building itself: The standard type-I orbifold model building only allows for a single model on this orbifold, while the blowup models give five different models in blow down.

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arXiv2003

Relativistic fluid mechanics, Kahler manifolds and supersymmetry

We propose an alternative for the Clebsch decomposition of currents in fluid mechanics, in terms of complex potentials taking values in a Kahler manifold. We reformulate classical relativistic fluid mechanics in terms of these complex potentials and rederive the existence of an infinite set of conserved currents. We perform a canonical analysis to find the explicit form of the algebra of conserved charges. The Kahler-space formulation of the theory has a natural supersymmetric extension in 4-D space-time. It contains a conserved current, but also a number of additional fields complicating the interpretation. Nevertheless, we show that an infinite set of conserved currents emerges in the vacuum sector of the additional fields. This sector can therefore be identified with a regime of supersymmetric fluid mechanics. Explicit expressions for the current and the density are obtained.

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arXiv2003

Traces on orbifolds: Anomalies and one-loop amplitudes

In the recent literature one can find calculations of various one--loop amplitudes, like anomalies, tadpoles and vacuum energies, on specific types of orbifolds, like S^1/Z_2. This work aims to give a general description of such one--loop computations for a large class of orbifold models. In order to achieve a high degree of generality, we formulate these calculations as evaluations of traces of operators over orbifold Hilbert spaces. We find that in general the result is expressed as a sum of traces over hyper surfaces with local projections, and the derivatives perpendicular to these hyper surfaces are rescaled. These local projectors naturally takes into account possible non--periodic boundary conditions. As the examples T^6/Z_4 and T^4/D_4 illustrate, the methods can be applied to non--prime as well as non--Abelian orbifolds.

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arXiv2003

Localized anomalies in heterotic orbifolds

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 x 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.

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arXiv2003

Localized tadpoles of anomalous heterotic U(1)'s

We investigate the properties of localized anomalous U(1)'s in heterotic string theory on the orbifold T^6/Z_3. We argue that the local four dimensional and original ten dimensional Green-Schwarz mechanisms can be implemented simultaneously, making the theory manifestly gauge invariant everywhere, in the bulk and at the fixed points. We compute the shape of the Fayet-Iliopoulos tadpoles, and cross check this derivation for the four dimensional auxiliary fields by a direct calculation of the tadpoles of the internal gauge fields. Finally we study some resulting consequences for spontaneous symmetry breaking, and derive the profile of the internal gauge field background over the orbifold.

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arXiv2003

String corrections to gauge couplings from a field theory approach

An effective field theory approach is introduced to compute one-loop radiative corrections to the gauge couplings due to Kaluza-Klein states associated with a two-torus compactification. The results are compared with those of the string in the field theory ``limit'' alpha'-> 0. The whole U and the leading T moduli dependence of the gauge dependent part of the string corrections to gauge couplings can be recovered using the effective field theory approach.

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arXiv2003

Singular supersymmetric sigma models

Supersymmetric non-linear sigma-models are described by a field dependent Kaehler metric determining the kinetic terms. In general it is not guaranteed that this metric is always invertible. Our aim is to investigate the symmetry structure of supersymmetric models in four dimensional space-time in which metric singularities occur. For this purpose we study a simple anomaly-free extension of the supersymmetric CP^1 model from a classical point of view. We show that the metric singularities can be regularized by the addition of a soft supersymmetry-breaking mass parameter.

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arXiv2002

Localization and anomalies on orbifolds

In this talk we discus some properties of supersymmetric theories on orbifolds in five dimensions. The structure of FI--tadpoles may lead to (strong) localization of charged bulk scalars. Orbifold theories may suffer from various kinds of anomalies. The parity anomaly may render the construction of the orbifold theory ill--defined. The gauge anomaly on the orbifold are localized at the fixed points, which can sometimes be canceled by a Chern--Simons term.

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arXiv2002

String Threshold corrections from Field Theory

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.

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arXiv2002

Instabilities of bulk fields and anomalies on orbifolds

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.

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arXiv2002

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 that purpose a basis for these perturbations determined by the background dynamics is introduced and multiple-field slow-roll functions are defined. To obtain analytic solutions to first order, the scalar perturbation modes have to be treated in three different regimes. Matching is performed by analytically identifying leading order asymptotic expansions in different regions. 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.

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