VTechWorks staff will be away for the winter holidays starting Tuesday, December 24, 2024, through Wednesday, January 1, 2025, and will not be replying to requests during this time. Thank you for your patience, and happy holidays!

Browsing by Author "Oehlmann, Paul-Konstantin"

Now showing 1 - 5 of 5
  • Thumbnail Image
    F-theory on quotient threefolds with (2,0) discrete superconformal matter
    Anderson, Lara B.; Grassi, Antonella; Gray, James A.; Oehlmann, Paul-Konstantin (Springer, 2018-06-20)
    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.
  • Thumbnail Image
    An F-theory realization of the chiral MSSM with Z(2)-parity
    Cvetič, Mirjam; Lin, Ling; Liu, Muyang; Oehlmann, Paul-Konstantin (Springer, 2018-09-17)
    Using F-theory we construct 4D 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) x 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 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 Z(2) into a U(1) and the resulting discrete anomalies.
  • Thumbnail Image
    Modular curves and Mordell-Weil torsion in F-theory
    Hajouji, Nadir; Oehlmann, Paul-Konstantin (2020-04-16)
    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 of torsion groups which can occur on a smooth elliptic Calabi-Yau n-fold is contained in the set of subgroups which appear on a rational elliptic surface if n >= 3 and is slightly larger for n = 2. The key idea in our proof is showing that any elliptic fibration with sufficiently large torsion(1) 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 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.
  • Thumbnail Image
    Mordell-Weil torsion in the mirror of multi-sections
    Oehlmann, Paul-Konstantin; Reuter, Jonas; Schimannek, Thorsten (Springer, 2016-12-12)
    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.
  • Thumbnail Image
    Twisted Fibrations in M/F-theory
    Anderson, Lara B.; Gray, James; Oehlmann, Paul-Konstantin (2024-01-04)
    In this work we investigate 5-dimensional theories obtained from M-theory on genus one fibered threefolds which exhibit twisted algebras in their fibers. We provide a base-independent algebraic description of the threefolds and compute light 5D BPS states charged under finite sub-algebras of the twisted algebras. We further construct the Jacobian fibrations that are associated to 6-dimensional F-theory lifts, where the twisted algebra is absent. These 6/5-dimensional theories are compared via twisted circle reductions of F-theory to M-theory. In the 5-dimensional theories we discuss several geometric transitions that connect twisted with untwisted fibrations. We present detailed discussions of 𝔢(2)6,𝔰𝔬(3)8 and 𝔰𝔲(2)3 twisted fibers and provide several explicit example threefolds via toric constructions. Finally, limits are considered in which gravity is decoupled, including Little String Theories for which we match 2-group symmetries across twisted T-dual theories.