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Elliptic Fibrations with Rank Three MordellWeil Group: Ftheory with U(1)×U(1)×U(1) Gauge Symmetry
, 2013
"... We analyze general Ftheory compactifications with U(1)xU(1)xU(1) Abelian gauge symmetry by constructing the general elliptically fibered CalabiYau manifolds with a rank three MordellWeil group of rational sections. The general elliptic fiber is shown to be a complete intersection of two nongen ..."
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We analyze general Ftheory compactifications with U(1)xU(1)xU(1) Abelian gauge symmetry by constructing the general elliptically fibered CalabiYau manifolds with a rank three MordellWeil group of rational sections. The general elliptic fiber is shown to be a complete intersection of two nongeneric quadrics in P3 and resolved elliptic fibrations are obtained by embedding the fiber as the generic CalabiYau complete intersection into Bl3P3, the blowup of P3 at three points. For a fixed base B, there are finitely many CalabiYau elliptic fibrations. Thus, Ftheory compactifications on these CalabiYau manifolds are shown to be labeled by integral points in reflexive polytopes constructed from the nefpartition of Bl3P3. 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 trifundamental 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 MordellWeil groups. We also compute explicitly the corresponding 14 multiplicities of massless hypermultiplets of a sixdimensional Ftheory compactification for a general base B.
Non abelian gauge symmetry and the Higgs mechanism in Ftheory. arXiv:1402.5962
"... Singular fiber resolution does not describe the spontaneous breaking of gauge symmetry in Ftheory, as the corresponding branch of the moduli space does not exist in the theory. Accordingly, even nonabelian gauge theories have not been fully understood in global Ftheory compactifications. We prese ..."
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Singular fiber resolution does not describe the spontaneous breaking of gauge symmetry in Ftheory, as the corresponding branch of the moduli space does not exist in the theory. Accordingly, even nonabelian gauge theories have not been fully understood in global Ftheory compactifications. We present a systematic discussion of using singularity deformation, which does describe the spontaneous breaking of gauge symmetry in Ftheory, to study nonabelian gauge symmetry. Since this branch of the moduli space also exists in the defining Mtheory compactification, it provides the only known description of gauge theory states which exists in both pictures; they are string junctions in Ftheory. Utilizing deformations, we study a number of new examples, including nonperturbative descriptions of SU(3) and SU(2) gauge theories on sevenbranes which do not admit a weakly coupled type IIb description. It may be of phenomenological interest that these nonperturbative descriptions do not exist for higher rank SU(N) theories. ar
Chiral FourDimensional FTheory Compactifications With SU(5) and Multiple U(1)Factors
, 2014
"... We develop geometric techniques to determine the spectrum and the chiral indices of matter multiplets for fourdimensional Ftheory compactifications on elliptic CalabiYau fourfolds with rank two MordellWeil group. The general elliptic fiber is the CalabiYau onefold in dP2. We classify its resol ..."
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We develop geometric techniques to determine the spectrum and the chiral indices of matter multiplets for fourdimensional Ftheory compactifications on elliptic CalabiYau fourfolds with rank two MordellWeil group. The general elliptic fiber is the CalabiYau onefold in dP2. 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)×U(1) and SU(5)×U(1)×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 = P3. We determine the general G4flux that belongs to H(2,2)V of the resolved CalabiYau fourfolds. As a byproduct, we derive for the first time all conditions on G4flux in general Ftheory compactifications with a nonholomorphic zero section. These conditions have to be formulated after a circle reduction in terms of ChernSimons terms on the 3D Coulomb branch and invoke Mtheory/Ftheory duality. New ChernSimons terms are generated by KaluzaKlein states of the circle compactification. We explicitly perform the relevant field theory computations, that yield nonvanishing results precisely for fourfolds with a nonholomorphic zero section. Taking into account the new ChernSimons terms, all 4D matter chiralities are determined via 3D Mtheory/Ftheory 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.
and its Higgs Branches
, 2014
"... We consider Ftheory compactifications on genusone fibered CalabiYau manifolds with their fibers realized as hypersurfaces in the toric varieties associated to the 16 reflexive 2D polyhedra. We present a baseindependent analysis of the codimension one, two and three singularities of these fibrati ..."
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We consider Ftheory compactifications on genusone fibered CalabiYau manifolds with their fibers realized as hypersurfaces in the toric varieties associated to the 16 reflexive 2D polyhedra. We present a baseindependent 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 nontrivial gauge group and matter content. We explore the network of Higgsings relating these theories. Such Higgsings geometrically correspond to extremal transitions induced by blowups in the 2D toric varieties. We recover the 6D effective theories of all 16 toric hypersurface fibrations by repeatedly Higgsing the theories that exhibit MordellWeil torsion. We find that the three CalabiYau manifolds without section, whose fibers are given by the toric hypersurfaces in P2, P1 × P1 and the recently studied P2(1, 1, 2), yield Ftheory realizations of SUGRA theories with discrete gauge groups Z3, Z2 and Z4. This opens up a whole new arena for model building with discrete global symmetries in Ftheory. In these three manifolds, we also find codimension two I2fibers 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 Ftheory. Furthermore, the elliptically fibered CalabiYau manifold based on dP1 has a U(1)gauge field induced by a nontoric rational section. In this model, we find the first Ftheory realization of matter with U(1)charge q = 3.
Prepared for submission to JHEP The CremmerScherk Mechanism in Ftheory Compactifications on K3 Manifolds
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On the Classification of 6D SCFTs and Generalized ADE Orbifolds
, 2013
"... We study (1, 0) and (2, 0) 6D superconformal field theories (SCFTs) that can be constructed in Ftheory. Quite surprisingly, all of them involve an orbifold singularity C2/Γ with Γ a discrete subgroup of U(2). When Γ is a subgroup of SU(2), all discrete subgroups are allowed, and this leads to the ..."
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We study (1, 0) and (2, 0) 6D superconformal field theories (SCFTs) that can be constructed in Ftheory. Quite surprisingly, all of them involve an orbifold singularity C2/Γ with Γ a discrete subgroup of U(2). When Γ is a subgroup of SU(2), all discrete subgroups are allowed, and this leads to the familiar ADE classification of (2, 0) SCFTs. For more general U(2) subgroups, the allowed possibilities for Γ are not arbitrary and are given by certain generalizations of the A and Dseries. These theories should be viewed as the minimal 6D SCFTs. We obtain all other SCFTs by bringing in a number of Estring theories and/or decorating curves in the base by nonminimal gauge algebras. In this way we obtain a vast number of new 6D SCFTs, and we conjecture that our construction provides a full list.
NonHiggsable clusters for 4D Ftheory models
, 2015
"... Abstract: We analyze nonHiggsable clusters of gauge groups and matter that can arise at the level of geometry in 4D Ftheory models. NonHiggsable clusters seem to be generic features of Ftheory compactifications, and give rise naturally to structures that include the nonabelian part of the standa ..."
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Abstract: We analyze nonHiggsable clusters of gauge groups and matter that can arise at the level of geometry in 4D Ftheory models. NonHiggsable clusters seem to be generic features of Ftheory compactifications, and give rise naturally to structures that include the nonabelian part of the standard model gauge group and certain specific types of potential dark matter candidates. In particular, there are nine distinct single nonabelian gauge group factors, and only five distinct products of two nonabelian gauge group factors with matter, including SU(3) × SU(2), that can be realized through 4D nonHiggsable clusters. There are also more complicated configurations involving more than two gauge factors; in particular, the collection of gauge group factors with jointly charged matter can exhibit branchings, loops, and long linear chains.