arXiv subjects

Patrick K. S. Vaudrevange

Publications and source records attributed to Patrick K. S. Vaudrevange.

At least 55 records · Page 3Linked to original sources

arXiv2012

The mu term and neutrino masses

The well-known Giudice-Masiero mechanism explains the presence of a mu term of the order of the gravitino mass, but does not explain why the holomorphic mass term is absent in the superpotential. We discuss anomaly-free discrete symmetries which are both compatible with SU(5) unification of matter and the Giudice-Masiero mechanism, i.e. forbid the mu term in the superpotential while allowing the necessary Kaehler potential term. We find that these are Z_M^R symmetries with the following properties: (i) M is a multiple of four; (ii) the Higgs bilinear H_u H_d transforms trivially; (iii) the superspace coordinate theta has charge M/4 and, accordingly, the superpotential has charge M/2; (iv) dimension five proton decay operators are automatically absent. All Z_M^R symmetries are anomaly-free due to a non-trivial transformation of a Green-Schwarz axion, and, as a consequence, a holomorphic mu term appears at the non-perturbative level. There is a unique symmetry that is consistent with the Weinberg operator while there is a class of Z_M^R symmetries which explain suppressed Dirac neutrino masses.

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arXiv2012

Origin of family symmetries

Discrete (family) symmetries might play an important role in models of elementary particle physics. We discuss the origin of such symmetries in the framework of consistent ultraviolet completions of the standard model in field and string theory. The symmetries can arise due to special geometrical properties of extra compact dimensions and the localization of fields in this geometrical landscape. We also comment on anomaly constraints for discrete symmetries.

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arXiv2011

The Orbifolder: A Tool to study the Low Energy Effective Theory of Heterotic Orbifolds

The orbifolder is a program developed in C++ that computes and analyzes the low-energy effective theory of heterotic orbifold compactifications. The program includes routines to compute the massless spectrum, to identify the allowed couplings in the superpotential, to automatically generate large sets of orbifold models, to identify phenomenologically interesting models (e.g. MSSM-like models) and to analyze their vacuum-configurations.

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arXiv2011

No-go theorems for R symmetries in four-dimensional GUTs

We prove that it is impossible to construct a grand unified model, based on a simple gauge group, in four dimensions that leads to the exact MSSM, nor to a singlet extension, and possesses an unbroken R symmetry. This implies that no MSSM model with either a Z_{M>=3}^R or U(1)_R symmetry can be completed by a four-dimensional GUT in the ultraviolet. However, our no-go theorem does not apply to GUT models with extra dimensions. We also show that it is impossible to construct a 4D GUT that leads to the MSSM plus an additional anomaly-free symmetry that forbids the mu term.

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arXiv2011

Discrete R symmetries for the MSSM and its singlet extensions

We determine the anomaly free discrete R symmetries, consistent with the MSSM, that commute with SU(5) and suppress the $μ$ parameter and nucleon decay. We show that the order M of such $Z_M^R$ symmetries has to divide 24 and identify 5 viable symmetries. The simplest possibility is a $Z_4^R$ symmetry which commutes with SO(10). We present a string-derived model with this $Z_4^R$ symmetry and the exact MSSM spectrum below the GUT scale; in this model $Z_4^R$ originates from the Lorentz symmetry of compactified dimensions. We extend the discussion to include the singlet extensions of the MSSM and find $Z_4^R$ and $Z_8^R$ are the only possible symmetries capable of solving the $μ$ problem in the NMSSM. We also show that a singlet extension of the MSSM based on a $Z_{24}^R$ symmetry can provide a simultaneous solution to the $μ$ and strong CP problem with the axion coupling in the favoured window.

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arXiv2010

String-derived MSSM vacua with residual R symmetries

Recently it was shown that there is a unique Z_4^R symmetry for the MSSM which allows the Yukawa couplings and dimension five neutrino mass operator, forbids the mu term and commutes with SO(10). This Z_4^R symmetry contains matter parity as a subgroup and forbids dimension four and five proton decay operators. We show how to construct string vacua with discrete R symmetries in general and this symmetry in particular, and present an explicit example which exhibits the exact MSSM spectrum, the Z_4^R symmetry as well as other desired features such as gauge-top unification. We introduce the Hilbert basis method for determining all D-flat configurations and efficient algorithms for identifying field configurations with a desired residual symmetry. These methods are used in an explicit example, in which we describe in detail how to construct a supersymmetric vacuum configuration with the phenomenologically attractive Z_4^R symmetry. At the perturbative level, this is a supersymmetric Minkowski vacuum in which almost all singlet fields (moduli) are fixed.

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arXiv2010

A unique Z_4^R symmetry for the MSSM

We consider the possible anomaly free Abelian discrete symmetries of the MSSM that forbid the mu-term at perturbative order. Allowing for anomaly cancellation via the Green-Schwarz mechanism we identify discrete R-symmetries as the only possibility and prove that there is a unique Z_4^R symmetry that commutes with SO(10). We argue that non-perturbative effects will generate a mu-term of electroweak order thus solving the mu-problem. The non-perturbative effects break the Z_4^R symmetry leaving an exact Z_2 matter parity. As a result dimension four baryon- and lepton-number violating operators are absent while, at the non-perturbative level, dimension five baryon- and lepton-number violating operators get induced but are highly suppressed so that the nucleon decay rate is well within present bounds.

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arXiv2010

Proton Hexality in Local Grand Unification

Proton hexality is a discrete symmetry that avoids the problem of too fast proton decay in the supersymmetric extension of the standard model. Unfortunately it is inconsistent with conventional grand unification. We show that proton hexality can be incorporated in the scheme of "Local Grand Unification" discussed in the framework of model building in (heterotic) string theory.

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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.

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arXiv2010

An involuted orbifold MSSM

A compactification of the E_8 x E_8 heterotic string on a Z_2 x Z_2 orbifold equipped with an additional freely acting involution is presented. This model reproduces the exact chiral MSSM spectrum with matter parity and a non-trivial Yukawa structure. The key ingredient is a freely acting Wilson line associated to the involution, breaking SU(5) to SU(3) x SU(2) x U(1)_Y. This work is based on a talk given at the "9th Hellenic School and Workshop on Elementary Particle Physics and Gravity" and reviews the results of a collaboration with M. Blaszczyk, S. Groot Nibbelink, M. Ratz, F. Ruehle and M. Trapletti.

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arXiv2010

Heterotic mini-landscape (II): completing the search for MSSM vacua in a Z_6 orbifold

We complete our search for MSSM vacua in the Z_6-II heterotic orbifold by including models with 3 Wilson lines. We estimate the total number of inequivalent models in this orbifold to be 10^7. Out of these, we find almost 300 models with the exact MSSM spectrum, gauge coupling unification and a heavy top quark. Models with these features originate predominantly from local GUTs. The scale of gaugino condensation in the hidden sector is correlated with properties of the observable sector such that soft masses in the TeV range are preferred.

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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.

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arXiv2009

Local Grand Unification and String Theory

The low energy effective action of string theory depends strongly on the process of compactification and the localization of fields in extra dimensions. Explicit string constructions towards the minimal supersymmetric standard model (MSSM) reveal interesting results leading to the concept of local grand unification. Properties of the MSSM indicate that we might live at a special location close to an orbifold fixed point rather than a generic point in Calabi-Yau moduli space. We observe an enhancement of (discrete) symmetries that have various implications for the properties of the MSSM such as proton stability as well as solutions to the flavor problem, the μ-problem and the strong CP-problem.

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arXiv2009

Accions

Axion fields provide the most elegant solution to the strong CP problem. In string compactifications it is difficult to obtain an axion whose decay constant is consistent with current cosmological bounds. We examine this question in theories with accidental U(1) symmetries that appear as low energy remnants of discrete symmetries. We refer to the axion-like particles from the spontaneous breakdown of these symmetries as accions. In such systems, the accion decay constant depends on the vacuum configuration and can be lowered to fit the bounds. Furthermore, we find that such accions with consistent decay constant can be embedded in special vacua of Z_6-II orbifold models with realistic features.

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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.

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arXiv2008

Grand Unification in the Heterotic Brane World

The compactification of the heterotic string on six-dimensional orbifolds is reviewed. Some important technical aspects of their construction are clarified and new parameters, called generalized discrete torsion, are introduced and related to the torsionless construction. Furthermore, a systematic search for MSSM-like models is performed in the context of Z6-II orbifolds, addressing questions like the identification of a supersymmetric vacuum with a naturally small mu-term and proton decay. Finally, the blow-up of Z3 singularities is discussed in the local and in the global case - also in the presence of Wilson lines. This procedure is exemplified with the resolution of a Z3 MSSM candidate.

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arXiv2008

Large hierarchies from approximate R symmetries

We show that hierarchically small vacuum expectation values of the superpotential in supersymmetric theories can be a consequence of an approximate R symmetry. We briefly discuss the role of such small constants in moduli stabilization and understanding the huge hierarchy between the Planck and electroweak scales.

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arXiv2008

(Non-)Abelian discrete anomalies

We derive anomaly constraints for Abelian and non-Abelian discrete symmetries using the path integral approach. We survey anomalies of discrete symmetries in heterotic orbifolds and find a new relation between such anomalies and the so-called `anomalous' U(1).

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