arXiv subjects

Stefan Groot Nibbelink

Publications and source records attributed to Stefan Groot Nibbelink.

At least 37 records · Page 2Linked to original sources

arXiv2013

Heterotic warped Eguchi-Hanson spectra with five-branes and line bundles

We consider heterotic strings on a warped Eguchi-Hanson space with five-brane and line bundle gauge fluxes. The heterotic string admits an exact CFT description in terms of an asymmetrically gauged SU(2)xSL(2,R) WZW model, in a specific double scaling limit in which the blow-up radius and the string scale are sent to zero simultaneously. This allows us to compute the perturbative 6D spectra for these models in two independent fashions: i) Within the supergravity approximation we employ a representation dependent index; ii) In the double scaling limit we determine all marginal vertex operators of the coset CFT. To achieve agreement between the supergravity and the CFT spectra, we conjecture that the untwisted and the twisted CFT states correspond to the same set of hyper multiplets in supergravity. This is in a similar spirit as a conjectured duality between asymptotically linear dilaton CFTs and little string theory living on NS-five-branes. As the five-brane charge is non-vanishing, heterotic (anti-)five-branes have to be added in order to cancel irreducible gauge anomalies. The local spectra can be combined in such a way that supersymmetry is preserved on the compact resolved T^4/Z_2 orbifold by choosing the local gauge fluxes appropriately.

hep-th↗

arXiv2013

Schoen manifold with line bundles as resolved magnetized orbifolds

We give an alternative description of the Schoen manifold as the blow-up of a Z2xZ2 orbifold in which one Z2 factor acts as a roto-translation. Since for this orbifold the fixed tori are only identified in pairs but not orbifolded, four-dimensional chirality can never be obtained in heterotic string compactifications using standard techniques alone. However, chirality is recovered when its tori become magnetized. To exemplify this, we construct an E8xE8' heterotic SU(5) GUT on the Schoen manifold with Abelian gauge fluxes, which becomes an MSSM with three generations after an appropriate Wilson line is associated to its freely acting involution. We reproduce this model as a standard heterotic orbifold CFT of the (partially) blown down Schoen manifold with a magnetic flux. Finally, in analogy to a proposal for non--perturbative heterotic models by Aldazabal et al. we suggest modifications to the heterotic orbifold spectrum formulae in the presence of magnetized tori.

hep-th↗

arXiv2012

A Lorentz invariant doubled worldsheet theory

We propose a Lorentz invariant version of Tseytlin's doubled worldsheet theory that makes T-duality covariance of the string manifest. This theory can be derived as a gauge fixed version of Buscher's gauging procedure, in which the left-over gauge field component acts as a Lagrange multiplier. This description can naturally account for fractional linear O(D,D) transformations of the metric and b-field. It is capable of describing non-geometric backgrounds; geometric and non-geometric fluxes are encoded in the doubled anti-symmetric tensor field strength.

hep-th↗

arXiv2012

Super Weyl invariance: BPS equations from heterotic worldsheets

It is well-known that the beta functions on a string worldsheet correspond to the target space equations of motion, e.g. the Einstein equations. We show that the BPS equations, i.e. the conditions of vanishing supersymmetry variations of the space-time fermions, can be directly derived from the worldsheet. To this end we consider the RNS-formulation of the heterotic string with (2,0) supersymmetry, which describes a complex torsion target space that supports a holomorphic vector bundle. After a detailed account of its quantization and renormalization, we establish that the cancellation of the Weyl anomaly combined with (2,0) finiteness implies the heterotic BPS conditions: At the one loop level the geometry is required to be conformally balanced and the gauge background has to satisfy the Hermitean Yang-Mills equations.

hep-th↗

arXiv2011

Gauged Linear Sigma Models for toroidal orbifold resolutions

Toroidal orbifolds and their resolutions are described within the framework of (2,2) Gauged Linear Sigma Models (GLSMs). Our procedure describes two-tori as hypersurfaces in (weighted) projective spaces. The description is chosen such that the orbifold singularities correspond to the zeros of their homogeneous coordinates. The individual orbifold singularities are resolved using a GLSM guise of non-compact toric resolutions, i.e. replacing discrete orbifold actions by Abelian worldsheet gaugings. Given that we employ the same global coordinates for both the toroidal orbifold and its resolutions, our GLSM formalism confirms the gluing procedure on the level of divisors discussed by Lust et al. Using our global GLSM description we can study the moduli space of such toroidal orbifolds as a whole. In particular, changes in topology can be described as phase transitions of the underlying GLSM. Finally, we argue that certain partially resolvable GLSMs, in which a certain number of fixed points can never be resolved, might be useful for the study of mini-landscape orbifold MSSMs.

hep-th↗

arXiv2011

Green-Schwarz Mechanism in Heterotic (2,0) Gauged Linear Sigma Models: Torsion and NS5 Branes

Heterotic string compactifications can be conveniently described in the language of (2,0) gauged linear sigma models (GLSMs). Such models allow for Fayet-Iliopoulos (FI)-terms, which can be interpreted as Kahler parameters and axions on the target space geometry. We show that field dependent non-gauge invariant FI-terms lead to a Green-Schwarz-like mechanism on the worldsheet which can be used to cancel worldsheet anomalies. However, given that these FI-terms are constrained by quantization conditions due to worldsheet gauge instantons, the anomaly conditions turn out to be still rather constraining. Field dependent non-gauge invariant FI-terms result in non-Kahler, i.e. torsional, target spaces in general. When FI-terms involve logarithmic terms, the GLSM seems to describe the heterotic string in the presence of Neveu-Schwarz (NS)5 branes. In particular, when the gauge bundle overcloses the Bianchi identities, the GLSM describes a decompactified target space geometry due to anti-NS5 branes.

hep-th↗

arXiv2011

Heterotic orbifold resolutions as (2,0) gauged linear sigma models

In this work we attempt to bridge the gap between heterotic orbifold models and Calabi-Yau compactifications using gauged linear sigma models (GLSMs) with (2,0) worldsheet supersymmetry. We associate a specific GLSM to a heterotic orbifold model with twisted states that have non-vanishing vacuum expectation values (VEVs): The charges of the GLSM superfields are essentially determined by the shifted momenta of these states. When a twisted state contains an oscillator excitation, a fermionic gauging is introduced on the worldsheet inducing a non-Abelian gauge bundle, e.g. the standard embedding. However, irrespectively of whether the twisted states contain oscillators or not, they can be interpreted as blow-up modes, as their VEVs are correlated with sizes of exceptional cycles in the resolved geometry. By considering marginal deformations of a GLSM in the large volume limit we are able to directly determine its effective four dimensional spectrum. In the cases considered the spectra coincide with those computed via index theorems.

hep-th↗

arXiv2010

Heterotic MSSM on a Resolved Orbifold

We construct an MSSM with three generations from the heterotic string compactified on a smooth 6D internal manifold using Abelian gauge fluxes only. The compactification space is obtained as a resolution of the T6/Z2xZ2xZ2-free orbifold. The Z2-free involution of such a resolution breaks the SU(5) GUT group down to the SM gauge group using a suitably chosen (freely acting) Wilson line. Surprisingly, the spectrum on a given resolution is larger than the one on the corresponding orbifold taking into account the branching and Higgsing due to the blow-up modes. The existence of extra resolution states is closely related to the fact that the resolution procedure is not unique. Rather, the various resolutions are connected to each other by flop transitions.

hep-th↗

arXiv2009

A Z2xZ2 standard model

We present a Z_2 x Z_2 orbifold compactification of the E_8 x E_8 heterotic string which gives rise to the exact chiral MSSM spectrum. The GUT breaking SU(5) to SU(3)_C x SU(2)_L x U(1)_Y is realized by modding out a freely acting symmetry. This ensures precision gauge coupling unification. Further, it allows us to break the GUT group without switching on flux in hypercharge direction, such that the standard model gauge bosons can remain massless when the orbifold singularities are blown up. The model has vacuum configurations with matter parity, a large top Yukawa coupling and other phenomenologically appealing features.

hep-th↗

arXiv2009

Heterotic Z6-II MSSM Orbifolds in Blowup

Heterotic orbifolds provide promising constructions of MSSM-like models in string theory. We investigate the connection of such orbifold models with smooth Calabi-Yau compactifications by examining resolutions of the T^6/Z6-II orbifold (which are far from unique) with Abelian gauge fluxes. These gauge backgrounds are topologically characterized by weight vectors of twisted states; one per fixed point or fixed line. The VEV's of these states generate the blowup from the orbifold perspective, and they reappear as axions on the blowup. We explain methods to solve the 24 resolution dependent Bianchi identities and present an explicit solution. Despite that a solution may contain the MSSM particle spectrum, the hypercharge turns out to be anomalous: Since all heterotic MSSM orbifolds analyzed so far have fixed points where only SM charged states appear, its gauge group can only be preserved provided that those singularities are not blown up. Going beyond the comparison of purely topological quantities (e.g. anomalous U(1) masses) may be hampered by the fact that in the orbifold limit the supergravity approximation to lowest order in alpha prime is breaking down.

hep-th↗

arXiv2008

Non-Abelian bundles on heterotic non-compact K3 orbifold blowups

Instantons on Eguchi-Hanson spaces provide explicit examples of stable bundles on non-compact four dimensional C^2/Z_n orbifold resolutions with non-Abelian structure groups. With this at hand, we can consider compactifications of ten dimensional SO(32) supergravity (arising as the low energy limit of the heterotic string) on the resolved spaces in the presence of non-Abelian bundles. We provide explicit examples in the resolved C^2/Z_3 case, and give a complete classification of all possible effective six dimensional models where the instantons are combined with Abelian gauge fluxes in order to fulfil the local Bianchi identity constraint. We compare these models with the corresponding C^2/Z_3 orbifold models, and find that all of these gauge backgrounds can be related to configurations of vacuum expectation values (VEV's) of twisted and sometimes untwisted states. Gauge groups and spectra are identical from both the orbifold and the smooth bundle perspectives.

hep-th↗

arXiv2008

Two loop effective kaehler potential of (non-)renormalizable supersymmetric models

We perform a supergraph computation of the effective Kaehler potential at one and two loops for general four dimensional N=1 supersymmetric theories described by arbitrary Kaehler potential, superpotential and gauge kinetic function. We only insist on gauge invariance of the Kaehler potential and the superpotential as we heavily rely on its consequences in the quantum theory. However, we do not require gauge invariance for the gauge kinetic functions, so that our results can also be applied to anomalous theories that involve the Green-Schwarz mechanism. We illustrate our two loop results by considering a few simple models: the (non-)renormalizable Wess-Zumino model and Super Quantum Electrodynamics.

hep-th↗

arXiv2008

Compact heterotic orbifolds in blow-up

We compare heterotic string models on orbifolds with supergravity models on smooth compact spaces, obtained by resolving the orbifold singularities. Our main focus is on heterotic E8xE8 models on the resolution of the compact T^6/Z_3 orbifold with Wilson lines. We explain how different gauge fluxes at various resolved fixed points can be interpreted in blow down as Wilson lines. Even when such Wilson lines are trivial from the orbifold perspective, they can still lead to additional symmetry breaking in blow-up. Full agreement is achieved between orbifold and resolved models, at the level of gauge interactions, massless spectrum and anomaly cancellation. In this matching the blow-up modes are of crucial importance: they play the role of model-dependent axions involved in the cancellation of multiple anomalous U(1)'s on the resolution. We illustrate various aspects by investigating blow-ups of a Z_3 MSSM model with two Wilson lines: if all its fixed points are resolved simultaneously, the SM gauge group is necessarily broken. Finally, we explore in detail the anomaly cancellation on the complex two dimensional resolution of C^2/Z_2.

hep-th↗

arXiv2007

Blowups of Heterotic Orbifolds using Toric Geometry

Heterotic orbifold models are promising candidates for models with MSSM like spectra. But orbifolds only correspond to a special place in moduli space, the bigger picture is described by the moduli space of Calabi-Yau spaces. In this talk we will make explicit connections between both points of view. To this end we study blowups of orbifold singularities using both explicit constructions and toric geometry techniques. We show that matching of all orbifold models in blowups are possible.

hep-th↗

arXiv2007

Toric Resolutions of Heterotic Orbifolds

We investigate resolutions of heterotic orbifolds using toric geometry. Our starting point is provided by the recently constructed heterotic models on explicit blowup of C^n/Z_n singularities. We show that the values of the relevant integrals, computed there, can be obtained as integrals of divisors (complex codimension one hypersurfaces) interpreted as (1,1)-forms in toric geometry. Motivated by this we give a self contained introduction to toric geometry for non-experts, focusing on those issues relevant for the construction of heterotic models on toric orbifold resolutions. We illustrate the methods by building heterotic models on the resolutions of C^2/Z_3, C^3/Z_4 and C^3/Z_2xZ_2'. We are able to obtain a direct identification between them and the known orbifold models. In the C^3/Z_2xZ_2' case we observe that, in spite of the existence of two inequivalent resolutions, fully consistent blowup models of heterotic orbifolds can only be constructed on one of them.

hep-th↗

arXiv2007

Nonlinear Properties of Vielbein Massive Gravity

We propose a non-linear extension of the Fierz-Pauli mass for the graviton through a functional of the vielbein and an external Minkowski background. The functional generalizes the notion of the measure, since it reduces to a cosmological constant if the external background is formally sent to zero. Such a term and the explicit external background, emerge dynamically from a bi--gravity theory, having both a massless and a massive graviton in its spectrum, in a specific limit in which the massless mode decouples, while the massive one couples universally to matter. We investigate the massive theory using the Stueckelberg method and providing a 't Hooft-Feynman gauge fixing in which the tensor, vector and scalar Stueckelberg fields decouple. We show that this model has the softest possible ultraviolet behavior which can be expected from any generic (Lorentz invariant) theory of massive gravity, namely that it becomes strong only at the scale Lambda_3 = (m_g^2 M_P)^{1/3}.

hep-th↗

arXiv2007

Effective Action of Softly Broken Supersymmetric Theories

We study the renormalization of (softly) broken supersymmetric theories at the one loop level in detail. We perform this analysis in a superspace approach in which the supersymmetry breaking interactions are parameterized using spurion insertions. We comment on the uniqueness of this parameterization. We compute the one loop renormalization of such theories by calculating superspace vacuum graphs with multiple spurion insertions. To preform this computation efficiently we develop algebraic properties of spurion operators, that naturally arise because the spurions are often surrounded by superspace projection operators. Our results are general apart from the restrictions that higher super covariant derivative terms and some finite effects due to non-commutativity of superfield dependent mass matrices are ignored. One of the soft potentials induces renormalization of the Kaehler potential.

hep-th↗

arXiv2006

Two Loop Effective Kaehler Potential

In this talk we study the renormalization of the effective Kaehler potential at one and two loops for general four dimensional (non--renormalizable) N=1 supersymmetric theories described by arbitrary Kaehler potential, superpotential and gauge kinetic function. We consider the Wess-Zumino model as an example.

hep-th↗