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: 27; Prenosov: 0 Polno 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: 31; Prenosov: 0 Polno 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: 45; Prenosov: 0 Polno besedilo (840,88 KB) |