1. General U(1) x U(1) F-theory compactifications and beyond: geometry of unHiggsings and novel matter structureMirjam Cvetič, Denis Klevers, Hernan Piragua, Washington Taylor, 2015, izvirni znanstveni članek Opis: We construct the general form of an F-theory compactification with two U(1) factors based on a general elliptically fibered Calabi-Yau manifold with Mordell-Weil group of rank two. This construction produces broad classes of models with diverse matter spectra, including many that are not realized in earlier F-theory constructions with U(1) x U(1) gauge symmetry. Generic U(1) x U(1) models can be related to a Higgsed non-Abelian model with gauge group SU(2) x SU(2) x SU(3), SU(2)(3) x SU(3), or a subgroup thereof. The nonlocal horizontal divisors of the Mordell-Weil group are replaced with local vertical divisors associated with the Cartan generators of non-Abelian gauge groups from Kodaira singularities. We give a global resolution of codimension two singularities of the Abelian model; we identify the full anomaly free matter content, and match it to the unHiggsed non-Abelian model. The non-Abelian Weierstrass model exhibits a new algebraic description of the singularities in the fibration that results in the first explicit construction of matter in the symmetric representation of SU(3). This matter is realized on double point singularities of the discriminant locus. The construction suggests a generalization to U(1)(k) factors with k > 2, which can be studied by Higgsing theories with larger non-Abelian gauge groups. Ključne besede: F-theory, differential geometry, algebraic geometry, gauge symmetry Objavljeno: 14.06.2017; Ogledov: 171; Prenosov: 34 Celotno besedilo (1,36 MB) |
2. Chiral four-dimensional F-theory compactifications with SU(5) and multiple U(1)-factorsMirjam Cvetič, Antonella Grassi, Denis Klevers, Hernan Piragua, 2014, izvirni znanstveni članek Opis: We develop geometric techniques to determine the spectrum and the chiral indices of matter multiplets for four-dimensional F-theory compactifications on elliptic Calabi-Yau fourfolds with rank two Mordell-Weil group. The general elliptic fiber is the Calabi-Yau onefold in dP(2). We classify its resolved elliptic fibrations over a general base B. The study of singularities of these fibrations leads to explicit matter representations, that we determine both for U(1) xU(1) and SU(5) x U(1) x U(1) constructions. We determine for the first time certain matter curves and surfaces using techniques involving prime ideals. The vertical cohomology ring of these fourfolds is calculated for both cases and general formulas for the Euler numbers are derived. Explicit calculations are presented for a specific base B = P-3. We determine the general G(4)-flux that belongs to H-V((2,2)) of the resolved Calabi-Yau fourfolds. As a by-product, we derive for the first time all conditions on G(4)-flux in general F-theory compactifications with a non-holomorphic zero section. These conditions have to be formulated after a circle reduction in terms of Chern-Simons terms on the 3D Coulomb branch and invoke M-theory/F-theory duality. New ChernSimons terms are generated by Kaluza-Klein states of the circle compactification. We explicitly perform the relevant field theory computations, that yield non-vanishing results precisely for fourfolds with a non-holomorphic zero section. Taking into account the new Chern-Simons terms, all 4D matter chiralities are determined via 3D M-theory/F-theory duality. We independently check these chiralities using the subset of matter surfaces we determined. The presented techniques are general and do not rely on toric data. Ključne besede: flux compactifications, F-theory Objavljeno: 27.06.2017; Ogledov: 130; Prenosov: 48 Celotno besedilo (1,75 MB) |
3. Elliptic fibrations with rank three Mordell-WeilgroupMirjam Cvetič, Denis Klevers, Hernan Piragua, Peng Song, 2014, izvirni znanstveni članek Opis: We analyze general F-theory compactifications with U(1)xU(1)xU(1) Abelian gauge symmetry by constructing the general elliptically fibered Calabi-Yau manifolds with a rank three Mordell-Weil group of rational sections. The general elliptic fiber is shown to be a complete intersection of two non-generic quadrics in P-3 and resolved elliptic fibrations are obtained by embedding the fiber as the generic Calabi-Yau complete intersection into Bl(3)P(3), the blow-up of P-3 at three points. For a fixed base B, there are finitely many Calabi-Yau elliptic fibrations. Thus, F-theory compactifications on these Calabi-Yau manifolds are shown to be labeled by integral points in reflexive polytopes constructed from the nef-partition of Bl(3)P(3). We determine all 14 massless matter representations to six and four dimensions by an explicit study of the codimension two singularities of the elliptic fibration. We obtain three matter representations charged under all three U(1)-factors, most notably a tri-fundamental representation. The existence of these representations, which are not present in generic perturbative Type II compactifications, signifies an intriguing universal structure of codimension two singularities of the elliptic fibrations with higher rank Mordell-Weil groups. We also compute explicitly the corresponding 14 multiplicities of massless hypermultiplets of a six-dimensional F-theory compactification for a general base B. Ključne besede: flux compactifications, F-theory, superstring vacua, D-branes Objavljeno: 27.06.2017; Ogledov: 182; Prenosov: 48 Celotno besedilo (840,88 KB) |
4. On finiteness of type IIB compactificationsMirjam Cvetič, James Halverson, Denis Klevers, Peng Song, 2014, izvirni znanstveni članek Opis: The string landscape satisfies interesting finiteness properties imposed by supersymmetry and string-theoretical consistency conditions. We study N = 1 supersymmetric compactifications of Type IIB string theory on smooth elliptically fibered Calabi-Yau threefolds at large volume with magnetized D9-branes and D5-branes. We prove that supersymmetry and tadpole cancellation conditions imply that there is a finite number of such configurations. In particular, we derive an explicitly computable bound on the number of magnetic flux quanta, as well as the number of D5-branes, which is independent of the continuous moduli of the setup. The proof applies if a number of easy to check geometric conditions of the twofold base are met. We show that these geometric conditions are satisfied for the almost Fano twofold bases given by each toric variety associated to a reflexive two-dimensional polytope as well as by the generic del Pezzo surfaces dP(n) with n = 0, ..., 8. Physically, this finiteness proof shows that there exist a finite collection of four-dimensional gauge groups and chiral matter spectra in the 4D supergravity theories realized by these compactifications. As a by-product we explicitly construct all generators of the Kaahler cones of dP(n) and work out their relation to representation theory. Ključne besede: black holes, supergravity, string theory, conformal field models, string duality Objavljeno: 27.06.2017; Ogledov: 225; Prenosov: 30 Celotno besedilo (1,01 MB) |
5. Origin of Abelian gauge symmetries in heterotic/F-theory dualityMirjam Cvetič, Antonella Grassi, Denis Klevers, Peng Song, Maximilian Poretschkin, 2016, izvirni znanstveni članek Opis: We study aspects of heterotic/F-theory duality for compactifications with Abelian gauge symmetries. We consider F-theory on general Calabi-Yau manifolds with a rank one Mordell-Weil group of rational sections. By rigorously performing the stable degeneration limit in a class of toric models, we derive both the Calabi-Yau geometry as well as the spectral cover describing the vector bundle in the heterotic dual theory. We carefully investigate the spectral cover employing the group law on the elliptic curve in the heterotic theory. We find in explicit examples that there are three different classes of heterotic duals that have U(1) factors in their low energy effective theories: split spectral covers describing bundles with S(U(m) x U(1)) structure group, spectral covers containing torsional sections that seem to give rise to bundles with SU(m) X Z(k) structure group and bundles with purely non-Abelian structure groups having a centralizer in E-8 containing a U(1) factor. In the former two cases, it is required that the elliptic fibration on the heterotic side has a non-trivial Mordell-Weil group. While the number of geometrically massless U(1)'s is determined entirely by geometry on the F-theory side, on the heterotic side the correct number of U(1)'s is found by taking into account a Stiickelberg mechanism in the lower-dimensional effective theory. In geometry, this corresponds to the condition that sections in the two half K3 surfaces that arise in the stable degeneration limit of F-theory can be glued together globally. Ključne besede: F-theory, string duality, superstrings, heterotic strings, M-theory Objavljeno: 27.06.2017; Ogledov: 293; Prenosov: 40 Celotno besedilo (1,15 MB) |
6. Three-family particle physics models from global F-theory compactificationsMirjam Cvetič, Denis Klevers, Damian Kaloni Mayorga Pena, Paul Oehlmann, Jonas Reuter, 2015, izvirni znanstveni članek Opis: 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 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 cancellation 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. Ključne besede: black holes, supergravity, string theory, conformal field models, string duality Objavljeno: 27.06.2017; Ogledov: 332; Prenosov: 39 Celotno besedilo (890,06 KB) |