arXiv subjects

Timo Weigand

Publications and source records attributed to Timo Weigand.

At least 73 records · Page 4Linked to original sources

arXiv2014

Chow groups, Deligne cohomology and massless matter in F-theory

We propose a method to compute the exact number of charged localized massless matter states in an F-theory compactification on a Calabi-Yau 4-fold with non-trivial 3-form data. Our starting point is the description of the 3-form data via Deligne cohomology. A refined cycle map allows us to specify concrete elements therein in terms of the second Chow group of the 4-fold, i.e. rational equivalence classes of algebraic 2-cycles. We use intersection theory within the Chow ring to extract from this data a line bundle class on the curves in the base of the fibration on which charged matter is localized. The associated cohomology groups are conjectured to count the exact massless spectrum, in agreement with general patterns in Type IIB compactifications with 7-branes. We exemplify our approach by calculating the massless spectrum in an SU(5) x U(1) toy model based on an elliptic 4-fold with an extra section. The explicit evaluation of the cohomology classes is performed with the help of the cohomCalg-algorithm by Blumenhagen et al.

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arXiv2014

SU(5) Tops with Multiple U(1)s in F-theory

We study F-theory compactifications with up to two Abelian gauge group factors that are based on elliptically fibered Calabi-Yau 4-folds describable as generic hypersurfaces. Special emphasis is put on elliptic fibrations based on generic Bl^2 P^2[3]-fibrations. These exhibit a Mordell-Weil group of rank two corresponding to two extra rational sections which give rise to two Abelian gauge group factors. We show that an alternative description of the same geometry as a complete intersection makes the existence of a holomorphic zero-section manifest, on the basis of which we compute the U(1) generators and a class of gauge fluxes. We analyse the fibre degenerations responsible for the appearance of localised charged matter states, whose charges, interactions and chiral index we compute geometrically. We implement an additional SU(5) gauge group by constructing the four inequivalent toric tops giving rise to SU(5) x U(1) x U(1) gauge symmetry and analyse the matter content. We demonstrate that notorious non-flat points can be avoided in well-defined Calabi-Yau 4-folds. These methods are applied to the remaining possible hypersurface fibrations with one generic Abelian gauge factor. We analyse the local limit of our SU(5) x U(1) x U(1) models and show that one of our models is not embeddable into E8 due to recombination of matter curves that cannot be described as a Higgsing of E8. We argue that such recombination forms a general mechanism that opens up new model building possibilities in F-theory.

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arXiv2013

The Higgs mass from a String-Theoretic Perspective

The Higgs quartic coupling has now been indirectly measured at the electroweak scale. Assuming no new low-scale physics, its running is known and, together with gauge and Yukawa couplings, it is a crucial new piece of information constraining UV completions of the Standard Model. In particular, supersymmetry broken at an intermediate or high energy scale with tan(beta)=1 (i.e. lambda=0) is consistent with present data and has an independent theoretical appeal. We analyze the possible string-theoretic motivations for tan(beta)=1 (including both the shift-symmetry and the more economical variant of a Z_2 symmetry) in a Higgs sector realized on either 6- or 7-branes. We identify specific geometries where lambda ~ 0 may arise naturally and specify the geometrical problems which need to be solved to determine its precise value in the generic case. We then analyze the radiative corrections to lambda. Finally we show that, in contrast to naive expectations, lambda<0 at the SUSY breaking scale is also possible. Specifically, string theory may produce an MSSM plus chiral singlet at a very high scale, which immediately breaks to a non-SUSY Standard Model with lambda<0. This classically unstable theory then becomes metastable through running towards the IR.

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arXiv2013

U(1) symmetries in F-theory GUTs with multiple sections

We present a systematic construction of F-theory compactifications with Abelian gauge symmetries in addition to a non-Abelian gauge group G. The formalism is generally applicable to models in global Tate form but we focus on the phenomenologically interesting case of G=SU(5). The Abelian gauge factors arise due to extra global sections resulting from a specific factorisation of the Tate polynomial which describes the elliptic fibration. These constructions, which accommodate up to four different U(1) factors, are worked out in detail for the two possible embeddings of a single U(1) factor into E8, usually denoted SU(5) x U(1)_X and SU(5) x U(1)_PQ. The resolved models can be understood either patchwise via a small resolution or in terms of a P_{1,1,2}[4] description of the elliptic fibration. We derive the U(1) charges of the fields from the geometry, construct the U(1) gauge fluxes and exemplify the structure of the Yukawa interaction points. A particularly interesting result is that the global SU(5) x U(1)_PQ model exhibits extra SU(5)-singlet states which are incompatible with a single global decomposition of the 248 of E8. The states in turn lead to new Yukawa type couplings which have not been considered in local model building.

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arXiv2013

Hypercharge Flux in IIB and F-theory: Anomalies and Gauge Coupling Unification

We analyse hypercharge flux GUT breaking in F-theory/Type IIB GUT models with regards to its implications for anomaly cancellation and gauge coupling unification. To this aim we exploit the Type IIB limit and consider 7-brane configurations that for the first time are guaranteed to exhibit net hypercharge flux restriction to matter curves. We show that local F-theory models with anomalies of type U(1)_Y-U(1)^2 in the massless spectrum can be consistent only if such additional U(1)s are globally geometrically massive (in the sense that they arise from non-Kahler deformations of the Calabi-Yau four-fold). Further, in such cases of geometrically massive U(1)s hypercharge flux can induce new anomalies of type U(1)_Y^2-U(1) in the massless spectrum, violating constraints in local models forbidding such anomalies. In particular this implies that it is possible to construct models exhibiting a U(1)_{PQ} global symmetry which have hypercharge flux doublet-triplet splitting and no further exotics. We also show that the known hypercharge flux induced splitting of the gauge couplings in IIB models at tree-level can be reduced by a factor of 5 by employing a more F-theoretic twisting of U(1) flux by hypercharge flux bringing it to well within MSSM 2-loop results. In the case of net restriction of hypercharge flux to matter curves this tree-level splitting becomes more involved, is tied to the vacuum expectation values of certain closed-string fields, and therefore gauge coupling unification becomes tied to the question of moduli stabilisation.

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arXiv2013

Elliptic fibrations for SU(5) x U(1) x U(1) F-theory vacua

Elliptic Calabi-Yau fibrations with Mordell-Weil group of rank two are constructed. Such geometries are the basis for F-theory compactifications with two abelian gauge groups in addition to non-abelian gauge symmetry. We present the elliptic fibre both as a Bl^2P^2[3]-fibration and in the birationally equivalent Weierstrass form. The spectrum of charged singlets and their Yukawa interactions are worked out in generality. This framework can be combined with the toric construction of tops to implement additional non-abelian gauge groups. We utilise the classification of tops to construct SU(5) x U(1) x U(1) gauge symmetries systematically and study the resulting geometries, presenting the defining equations, the matter curves and their charges, the Yukawa couplings and explaining the process in detail for an example. Brane recombination relates these geometries to a Bl^1P^2[3]-fibration with a corresponding class of SU(5) x U(1) models. We also present the SU(5) tops based on the elliptic fibre Bl^1P_[1,1,2][4], corresponding to another class of SU(5) x U(1) models.

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arXiv2013

Fluxbranes: Moduli Stabilisation and Inflation

Fluxbrane inflation is a stringy version of D-term inflation in which two fluxed D7-branes move towards each other until their (relative) gauge flux annihilates. Compared to brane-antibrane inflation, the leading-order inflationary potential of this scenario is much flatter. In the present paper we first discuss a new explicit moduli stabilisation procedure combining the F- and D-term scalar potentials: It is based on fluxed D7-branes in a geometry with three large four-cycles of hierarchically different volumes. Subsequently, we combine this moduli stabilisation with the fluxbrane inflation idea, demonstrating in particular that CMB data (including cosmic string constraints) can be explained within our setup of hierarchical large volume CY compactifications. We also indicate how the eta-problem is expected to re-emerge through higher-order corrections and how it might be overcome by further refinements of our model. Finally, we explain why recently raised concerns about constant FI terms do not affect the consistent, string-derived variant of D-term inflation discussed in this paper.

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arXiv2012

Gauge Fluxes in F-theory and Type IIB Orientifolds

We provide a detailed correspondence between G_4 gauge fluxes in F-theory compactifications with SU(n) and SU(n)x(1) gauge symmetry and their Type IIB orientifold limit. Based on the resolution of the relevant F-theory Tate models we classify the factorisable G_4-fluxes and match them with the set of universal D5-tadpole free U(1)-fluxes in Type IIB. Where available, the global version of the universal spectral cover flux corresponds to Type IIB gauge flux associated with a massive diagonal U(1). In U(1)-restricted Tate models extra massless abelian fluxes exist which are associated with specific linear combinations of Type IIB fluxes. Key to a quantitative match between F-theory and Type IIB is a proper treatment of the conifold singularity encountered in the Sen limit of generic F-theory models. We also shed further light on the brane recombination process relating generic and U(1)-restricted Tate models.

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arXiv2012

Fluxed M5-instantons in F-theory

We analyse the non-perturbative superpotential due to M5-brane instantons in F-theory compactifications on Calabi-Yau fourfolds. The M5 partition function is obtained via holomorphic factorisation by explicitly performing the sum over chiral 3-form fluxes. Comparison with the partition function of fluxed Euclidean D3-brane instantons in Type IIB orientifolds allows us to fix the spin structure on the intermediate Jacobian of the M5-instanton. We furthermore analyse the contribution of the M5-instanton to the superpotential in the presence of G4 gauge flux, where the superpotential is dressed with matter fields. We explicitly evaluate the pullback of G4 onto the M5-brane as a measure for the presence of charged instanton zero modes. This accounts for the M5 charge both under massless U(1)s, if present, and under what corresponds in Type II language to geometrically massive U(1)s.

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arXiv2012

A Shift Symmetry in the Higgs Sector: Experimental Hints and Stringy Realizations

We interpret reported hints of a Standard Model Higgs boson at ~ 125 GeV in terms of high-scale supersymmetry breaking with a shift symmetry in the Higgs sector. More specifically, the Higgs mass range suggested by recent LHC data extrapolates, within the (non-supersymmetric) Standard Model, to a vanishing quartic Higgs coupling at a UV scale between 10^6 and 10^18 GeV. Such a small value of lambda can be understood in terms of models with high-scale SUSY breaking if the Kahler potential possesses a shift symmetry, i.e., if it depends on H_u and H_d only in the combination (H_u+\bar{H}_d). This symmetry is known to arise rather naturally in certain heterotic compactifications. We suggest that such a structure of the Higgs Kahler potential is common in a wider class of string constructions, including intersecting D7- and D6-brane models and their extensions to F-theory or M-theory. The latest LHC data may thus be interpreted as hinting to a particular class of compactifications which possess this shift symmetry.

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arXiv2011

G_4 flux, chiral matter and singularity resolution in F-theory compactifications

We construct a set of chirality inducing G_4-fluxes in global F-theory compactifications on Calabi-Yau four-folds. Special emphasis is put on models with gauge group SU(5) x U(1)_X relevant in the context of F-theory GUT model building, which are described in terms of a U(1)-restricted Tate model. In this type of constructions, the G_4-flux arises in a manner completely analogous to the U(1)_X gauge potential. We describe in detail the resolution by blow-up of the various singularities responsible for the U(1)_X factor and the standard SU(5) gauge group and match the result with techniques applied in the context of toric geometry. This provides an explicit identification of the structure of the resolved fibre over the matter curves and over the enhancement points relevant for Yukawa couplings. The U(1)_X flux induces a chiral matter spectrum. We compute the chiral index both of SU(5) charged matter and of SU(5) singlets charged only under U(1)_X localised on curves which are not contained in the SU(5) locus. We furthermore discuss global consistency conditions such as D3-tadpole cancellation, D-term supersymmetry and Freed-Witten quantisation. The U(1)_X gauge flux is a global extension of a class of split spectral cover bundles. It constitutes an essential ingredient in the construction of globally defined F-theory compactifications with chiral matter. We exemplify this in a three-generation SU(5) x U(1)_X model whose flux satisfies all of the above global consistency conditions. We also extend our results to chiral fluxes in models without U(1) restriction.

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arXiv2011

Fluxbrane Inflation

As a first step towards inflation in genuinely F-theoretic setups, we propose a scenario where the inflaton is the relative position of two 7-branes on holomorphic 4-cycles. Non-supersymmetric gauge flux induces an attractive inter-brane potential. The latter is sufficiently flat in the supergravity regime of large volume moduli. Thus, in contrast to brane-antibrane inflation, fluxbrane inflation does not require warping. We calculate the inflaton potential both in the supergravity approximation and via an open-string one-loop computation on toroidal backgrounds. This leads us to propose a generalisation to genuine Calabi-Yau manifolds. We also comment on competing F-term effects. The end of inflation is marked by the condensation of tachyonic recombination fields between the 7-branes, triggering the formation of a bound state described as a stable extension along the 7-brane divisor. Hence our model fits in the framework of hybrid D-term inflation. We work out the main phenomenological properties of our D-term inflaton potential. In particular, our scenario of D7/D7 inflation avoids the familiar observational constraints associated with cosmic strings.

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arXiv2011

Massive Abelian Gauge Symmetries and Fluxes in F-theory

F-theory compactified on a Calabi-Yau fourfold naturally describes non-Abelian gauge symmetries through the singularity structure of the elliptic fibration. In contrast Abelian symmetries are more difficult to study because of their inherently global nature. We argue that in general F-theory compactifications there are massive Abelian symmetries, such as the uplift of the Abelian part of the U(N) gauge group on D7-branes, that arise from non-Kahler resolutions of the dual M-theory setup. The four-dimensional F-theory vacuum with vanishing expectation values for the gauge fields corresponds to the Calabi-Yau limit. We propose that fluxes that are turned on along these U(1)s are uplifted to non-harmonic four-form fluxes. We derive the effective four-dimensional gauged supergravity resulting from F-theory compactifications in the presence of the Abelian gauge factors including the effects of possible fluxes on the gauging, tadpoles and matter spectrum.

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arXiv2011

On Fluxed Instantons and Moduli Stabilisation in IIB Orientifolds and F-theory

We study the superpotential induced by Euclidean D3-brane instantons carrying instanton flux, with special emphasis on its significance for the stabilisation of Kahler moduli and Neveu-Schwarz axions in Type IIB orientifolds. Quite generally, once a chiral observable sector is included in the compactification, arising on intersecting D7-branes with world-volume flux, resulting charged instanton zero modes prevent a class of instantons from participating in moduli stabilisation. We show that instanton flux on Euclidean D3-branes can remove these extra zero modes and helps in reinstating full moduli stabilisation within a geometric regime. We comment also on the F-theoretic description of this effect of alleviating the general tension between moduli stabilisation and chirality. In addition we propose an alternative solution to this problem based on dressing the instantons with charged matter fields which is unique to F-theory and cannot be realised in the weak coupling limit.

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arXiv2011

The effective action of D6-branes in N=1 type IIA orientifolds

We use a Kaluza-Klein reduction to compute the low-energy effective action for the massless modes of a spacetime-filling D6-brane wrapped on a special Lagrangian 3-cycle of a type IIA Calabi-Yau orientifold. The modifications to the characteristic data of the N=1 bulk orientifold theory in the presence of a D6-brane are analysed by studying the underlying Type IIA supergravity coupled to the brane worldvolume in the democratic formulation and performing a detailed dualisation procedure. The N=1 chiral coordinates are found to be in agreement with expectations from mirror symmetry. We work out the Kahler potential for the chiral superfields as well as the gauge kinetic functions for the bulk and the brane gauge multiplets including the kinetic mixing between the two. The scalar potential resulting from the dualisation procedure can be formally interpreted in terms of a superpotential. Finally, the gauging of the Peccei-Quinn shift symmetries of the complex structure multiplets reproduces the D-term potential enforcing the calibration condition for special Lagrangian 3-cycles.

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arXiv2010

Lectures on F-theory compactifications and model building

These lecture notes are devoted to formal and phenomenological aspects of F-theory. We begin with a pedagogical introduction to the general concepts of F-theory, covering classic topics such as the connection to Type IIB orientifolds, the geometry of elliptic fibrations and the emergence of gauge groups, matter and Yukawa couplings. As a suitable framework for the construction of compact F-theory vacua we describe a special class of Weierstrass models called Tate models, whose local properties are captured by the spectral cover construction. Armed with this technology we proceed with a survey of F-theory GUT models, aiming at an overview of basic conceptual and phenomenological aspects, in particular in connection with GUT breaking via hypercharge flux.

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arXiv2010

On Abelian Gauge Symmetries and Proton Decay in Global F-theory GUTs

The existence of abelian gauge symmetries in four-dimensional F-theory compactifications depends on the global geometry of the internal Calabi-Yau fourfold and has important phenomenological consequences. We study conceptual and phenomenological aspects of such U(1) symmetries along the Coulomb and the Higgs branch. As one application we examine abelian gauge factors arising after a certain global restriction of the Tate model that goes beyond a local spectral cover analysis. In SU(5) GUT models this mechanism enforces a global U(1)_X symmetry that prevents dimension-4 proton decay and allows for an identification of candidate right-handed neutrinos. We invoke a detailed account of the singularities of Calabi-Yau fourfolds and their mirror duals starting from an underlying E_8 and E_7 x U(1) enhanced Tate model. The global resolutions and deformations of these singularities can be used as the appropriate framework to analyse F-theory GUT models.

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arXiv2009

F-Theory GUT Vacua on Compact Calabi-Yau Fourfolds

We present compact three-generation F-theory GUT models meeting in particular the constraints of D3-tadpole cancellation and D-term supersymmetry. To this end we explicitly construct elliptically fibered Calabi-Yau fourfolds as complete intersections in a toric ambient space. Toric methods enable us to control the singular geometry of the SU(5) GUT model. The GUT brane wraps a non-generic del Pezzo surface admitting GUT symmetry breaking via hypercharge flux. It is contractible to a curve and we demonstrate the existence of a consistent decoupling limit. We compute the Euler characteristic of the singular Calabi-Yau fourfold to show that our three-generation flux solutions obtained via the spectral cover construction are consistent with D3-tadpole cancellation.

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