arXiv subjects

Paul-Konstantin Oehlmann

Publications and source records attributed to Paul-Konstantin Oehlmann.

32 records · Page 2Linked to original sources

arXiv2019

GV-Spectroscopy for F-theory on genus-one fibrations

We present a novel technique to obtain base independent expressions for the matter loci of fibrations of complete intersection Calabi-Yau onefolds in toric ambient spaces. These can be used to systematically construct elliptically and genus one fibered Calabi-Yau $d$-folds that lead to desired gauge groups and spectra in F-theory. The technique, which we refer to as GV-spectroscopy, is based on the calculation of fiber Gopakumar-Vafa invariants using the Batyrev-Borisov construction of mirror pairs and application of the so-called Frobenius method to the data of a parametrized auxiliary polytope. In particular for fibers that generically lead to multiple sections, only multi-sections or that are complete intersections in higher codimension, our technique is vastly more efficient than classical approaches. As an application we study two Higgs chains of six-dimensional supergravities that are engineered by fibrations of codimension two complete intersection fibers. Both chains end on a vacuum with $G=\mathbb{Z}_4$ that is engineered by fibrations of bi-quadrics in $\mathbb{P}^3$. We use the detailed knowledge of the structure of the reducible fibers that we obtain from GV-spectroscopy to comment on the corresponding Tate-Shafarevich group. We also show that for all fibers the six-dimensional supergravity anomalies including the discrete anomalies generically cancel.

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arXiv2019

Modular Curves and Mordell-Weil Torsion in F-theory

In this work we prove a bound for the torsion in Mordell-Weil groups of smooth elliptically fibered Calabi-Yau 3- and 4-folds. In particular, we show that the set which can occur on a smooth elliptic Calabi-Yau $n$-fold for ($n\geq 3$) is contained in the set of subgroups which appear on a rational elliptic surface, and is slightly larger for $n = 2$. The key idea in our proof is showing that any elliptic fibration with sufficiently large torsion has singularities in codimension 2 which do not admit a crepant resolution. We prove this by explicitly constructing and studying maps to a modular curve whose existence is predicted by a universal property. We use the geometry of modular curves to explain the minimal singularities that appear on an elliptic fibration with prescribed torsion, and to determine the degree of the fundamental line bundle (hence the Kodaira dimension) of the universal elliptic surface which we show to be consistent with explicit Weierstrass models. The constraints from the modular curves are used to bound the first fundamental group of any gauge group $G$ in a supergravity theory obtained from F-theory. We comment on the isolated 8-dimensional theories, obtained from extremal K3's, that are able to circumvent lower dimensional bounds. These theories neither have a heterotic dual, nor can they be compactified to lower dimensional minimal SUGRA theories. We also comment on the maximal, discrete gauged symmetries obtained from certain Calabi-Yau threefold quotients.

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arXiv2019

F-Theory on Quotients of Elliptic Calabi-Yau Threefolds

In this work we consider quotients of elliptically fibered Calabi-Yau threefolds by freely acting discrete groups and the associated physics of F-theory compactifications on such backgrounds. The process of quotienting a Calabi-Yau geometry produces not only new genus one fibered manifolds, but also new effective 6-dimensional physics. These theories can be uniquely characterized by the much simpler covering space geometry and the symmetry action on it. We use this method to construct examples of F-theory models with an array of discrete gauge groups and non-trivial monodromies, including an example with Z6 discrete symmetry.

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arXiv2018

Global tensor-matter transitions in F-theory

We use F-theory to study gauge algebra preserving transitions of 6d supergravity theories that are connected by superconformal points. While the vector multiplets remain unchanged, the hyper- and tensor multiplet sectors are modified. In 6d F-theory models, these transitions are realized by tuning the intersection points of two curves, one of them carrying a non-Abelian gauge algebra, to a (4,6,12) singularity, followed by a resolution in the base. The six-dimensional supergravity anomaly constraints are strong enough to completely fix the possible non-Abelian representations and to restrict the Abelian charges in the hypermultiplet sector affected by the transition, as we demonstrate for all Lie algebras and their representations. Furthermore, we present several examples of such transitions in torically resolved fibrations. In these smooth models, superconformal points lead to non-flat fibers which correspond to non-toric Kähler deformations of the torus-fibered Calabi-Yau 3-fold geometry.

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arXiv2018

F-theory on Quotient Threefolds with (2,0) Discrete Superconformal Matter

We explore 6-dimensional compactifications of F-theory exhibiting (2,0) superconformal theories coupled to gravity that include discretely charged superconformal matter. Beginning with F-theory geometries with Abelian gauge fields and superconformal sectors, we provide examples of Higgsing transitions which break the $U(1)$ gauge symmetry to a discrete remnant in which the matter fields are also non-trivially coupled to a (2,0) SCFT. In the compactification background this corresponds to a geometric transition linking two fibered Calabi-Yau geometries defined over a singular base complex surface. An elliptically fibered Calabi-Yau threefold with non-zero Mordell-Weil rank can be connected to a smooth non-simply connected genus one fibered geometry constructed as a Calabi-Yau quotient. These hyperconifold transitions exhibit multiple fibers in co-dimension 2 over the base.

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arXiv2018

The Toric SO(10) F-Theory Landscape

Supergravity theories in more than four dimensions with grand unified gauge symmetries are an important intermediate step towards the ultraviolet completion of the Standard Model in string theory. Using toric geometry, we classify and analyze six-dimensional F-theory vacua with gauge group SO(10) taking into account Mordell-Weil U(1) and discrete gauge factors. We determine the full matter spectrum of these models, including charged and neutral SO(10) singlets. Based solely on the geometry, we compute all matter multiplicities and confirm the cancellation of gauge and gravitational anomalies independent of the base space. Particular emphasis is put on symmetry enhancements at the loci of matter fields and to the frequent appearance of superconformal points. They are linked to non-toric Kähler deformations which contribute to the counting of degrees of freedom. We compute the anomaly coefficients for these theories as well by using a base-independent blow-up procedure and superconformal matter transitions. Finally, we identify six-dimensional supergravity models which can yield the Standard Model with high-scale supersymmetry by further compactification to four dimensions in an Abelian flux background.

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arXiv2018

An F-theory Realization of the Chiral MSSM with $\mathbb{Z}_2$-Parity

Using F-theory we construct 4D ${\cal N}=1$ SUGRA theories with the Standard Model gauge group, three chiral generations, and matter parity in order to forbid all dimension four baryon and lepton number violating operators. The underlying geometries are derived by constructing smooth genus-one fibered Calabi--Yau fourfolds using toric tops that have a Jacobian fibration with rank one Mordell--Weil group and $SU(3) \times SU(2) $ singularities. The necessary gauge backgrounds on the smooth fourfolds are shown to be fully compatible with the quantization condition, including positive integer D3-tadpoles. This construction realizes for the first time a consistent UV completion of an MSSM-like model with matter parity in F-theory. Moreover our construction is general enough to also exhibit other relevant $\mathbb{Z}_2$ charge extensions of the MSSM such as lepton and baryon parity. Such models however are rendered inconsistent by non-integer fluxes, which are necessary for producing the exact MSSM chiral spectrum. These inconsistencies turn out to be intimately related to field theory considerations regarding a UV-embedding of the $\mathbb{Z}_2$ into a $U(1)$ and the resulting discrete anomalies.

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arXiv2016

Mordell-Weil Torsion in the Mirror of Multi-Sections

We give further evidence that genus-one fibers with multi-sections are mirror dual to fibers with Mordell-Weil torsion. In the physics of F-theory compactifications this implies a relation between models with a non-simply connected gauge group and those with discrete symmetries. We provide a combinatorial explanation of this phenomenon for toric hypersurfaces. In particular this leads to a criterion to deduce Mordell-Weil torsion directly from the polytope. For all 3134 complete intersection genus-one curves in three-dimensional toric ambient spaces we confirm the conjecture by explicit calculation. We comment on several new features of these models: The Weierstrass forms of many models can be identified by relabeling the coefficient sections. This reduces the number of models to 1024 inequivalent ones. We give an example of a fiber which contains only non-toric sections one of which becomes toric when the fiber is realized in a different ambient space. Similarly a singularity in codimension one can have a toric resolution in one representation while it is non-toric in another. Finally we give a list of 24 inequivalent genus-one fibers that simultaneously exhibit multi-sections and Mordell-Weil torsion in the Jacobian. We discuss a self-mirror example from this list in detail.

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arXiv2015

Tracing symmetries and their breakdown through phases of heterotic (2,2) compactifications

We are considering the class of heterotic $\mathcal{N}=(2,2)$ Landau-Ginzburg orbifolds with 9 fields corresponding to $A_1^9$ Gepner models. We classify all of its Abelian discrete quotients and obtain 152 inequivalent models closed under mirror symmetry with $\mathcal{N}=1,2$ and $4$ supersymmetry in 4D. We compute the full massless matter spectrum at the Fermat locus and find a universal relation satisfied by all models. In addition we give prescriptions of how to compute all quantum numbers of the 4D states including their discrete R-symmetries. Using mirror symmetry of rigid geometries we describe orbifold and smooth Calabi-Yau phases as deformations away from the Landau-Ginzburg Fermat locus in two explicit examples. We match the non-Fermat deformations to the 4D Higgs mechanism and study the conservation of R-symmetries. The first example is a $\mathbb{Z}_3$ orbifold on an E$_6$ lattice where the R-symmetry is preserved. Due to a permutation symmetry of blow-up and torus Kähler parameters the R-symmetry stays conserved also smooth Calabi-Yau phase. In the second example the R-symmetry gets broken once we deform to the geometric $\mathbb{Z}_3 \times \mathbb{Z}_{3,\text{free}}$ orbifold regime.

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arXiv2015

Three-Family Particle Physics Models from Global F-theory Compactifications

We construct four-dimensional, globally consistent F-theory models with three chiral generations, whose gauge group and matter representations coincide with those of the Minimal Supersymmetric Standard Model, the Pati-Salam Model and the Trinification Model. These models result from compactification on toric hypersurface fibrations $X$ with the choice of base $\mathbb{P}^3$. We observe that the F-theory conditions on the $G_4$-flux restrict the number of families to be at least three. We comment on the phenomenology of the models, and for Pati-Salam and Trinification models discuss the Higgsing to the Standard Model. A central point of this work is the construction of globally consistent $G_4$-flux. For this purpose we compute the vertical cohomology $H_V^{(2,2)}(X)$ in each case and solve the conditions imposed by matching the M- and F-theoretical 3D Chern-Simons terms. We explicitly check that the expressions found for the $G_4$-flux allow for a cancelation of D3-brane tadpoles. We also use the integrality of 3D Chern-Simons terms to ensure that our $G_4$-flux solutions are adequately quantized.

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arXiv2014

F-Theory on all Toric Hypersurface Fibrations and its Higgs Branches

We consider F-theory compactifications on genus-one fibered Calabi-Yau manifolds with their fibers realized as hypersurfaces in the toric varieties associated to the 16 reflexive 2D polyhedra. We present a base-independent analysis of the codimension one, two and three singularities of these fibrations. We use these geometric results to determine the gauge groups, matter representations, 6D matter multiplicities and 4D Yukawa couplings of the corresponding effective theories. All these theories have a non-trivial gauge group and matter content. We explore the network of Higgsings relating these theories. Such Higgsings geometrically correspond to extremal transitions induced by blow-ups in the 2D toric varieties. We recover the 6D effective theories of all 16 toric hypersurface fibrations by repeatedly Higgsing the theories that exhibit Mordell-Weil torsion. We find that the three Calabi-Yau manifolds without section, whose fibers are given by the toric hypersurfaces in P^2, P^1x P^1 and the recently studied P^2(1,1,2), yield F-theory realizations of SUGRA theories with discrete gauge groups Z_3, Z_2 and Z_4. This opens up a whole new arena for model building with discrete global symmetries in F-theory. In these three manifolds, we also find codimension two I_2-fibers supporting matter charged only under these discrete gauge groups. Their 6D matter multiplicities are computed employing ideal techniques and the associated Jacobian fibrations. We also show that the Jacobian of the biquadric fibration has one rational section, yielding one U(1)-gauge field in F-theory. Furthermore, the elliptically fibered Calabi-Yau manifold based on dP_1 has a U(1)-gauge field induced by a non-toric rational section. In this model, we find the first F-theory realization of matter with U(1)-charge q=3.

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arXiv2014

Rational F-Theory GUTs without exotics

We construct F-theory GUT models without exotic matter, leading to the MSSM matter spectrum with potential singlet extensions. The interplay of engineering explicit geometric setups, absence of four-dimensional anomalies, and realistic phenomenology of the couplings places severe constraints on the allowed local models in a given geometry. In constructions based on the spectral cover we find no model satisfying all these requirements. We then provide a survey of models with additional U(1) symmetries arising from rational sections of the elliptic fibration in toric constructions and obtain phenomenologically appealing models based on SU(5) tops. Furthermore we perform a bottom-up exploration beyond the toric section constructions discussed in the literature so far and identify benchmark models passing all our criteria, which can serve as a guideline for future geometric engineering.

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arXiv2013

Lessons from an Extended Heterotic Mini-Landscape

We consider the key ingredients which made the Z_6II Mini-Landscape a successful ground for model building. There one observes a preferred distribution for the fields of the standard model which has direct implications on the phenomenology, since it favors a heavy top quark and a plausible solution to the $μ$-problem. We extend the exploration to the Z_2xZ_4 orbifold, where a similar pattern is identified. To illustrate our findings we present an explicit Z_2xZ_4 model that exhibits the MSSM spectrum plus vector-like exotics at the orbifold point. We take this construction as an example of a larger class of orbifold models which were anticipated at the GUT level. Furthermore we comment on VEV configurations to decouple the exotics while maintaining a meaningful R-symmetry which could forbid the mu-term.

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arXiv2013

A Zip-code for Quarks, Leptons and Higgs Bosons

The location of matter fields and the pattern of gauge symmetry in extra dimensions are crucial ingredients for string model building. We analyze realistic MSSM models from the heterotic Z6 Mini-Landscape and extract those properties that are vital for their success. We find that Higgs bosons and the top quark are not localized in extra dimensions and live in the full D=10 dimensional space-time. The first two families of quarks and leptons, however, live at specific fixed points in extra dimensional space and exhibit a (discrete) family symmetry. Within a newly constructed Z2XZ4 orbifold framework we further elaborate on these location properties and the appearance of discrete symmetries. A similar geometrical picture emerges. This particular Zip-code for quarks, leptons and Higgs bosons seems to be of more general validity and thus a useful guideline for realistic model building in string theory.

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