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27
New Global Ftheory GUTs with U(1) symmetries
"... We construct global Ftheory GUTs with SU(5)×U(1) gauge group defined by specifying a fully resolved CalabiYau fourfold and consistent fourform Gflux. Its specific U(1) charged matter spectrum allows the desired Yukawa couplings, but forbids dangerous proton decay operators. The model we find: (1 ..."
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We construct global Ftheory GUTs with SU(5)×U(1) gauge group defined by specifying a fully resolved CalabiYau fourfold and consistent fourform Gflux. Its specific U(1) charged matter spectrum allows the desired Yukawa couplings, but forbids dangerous proton decay operators. The model we find: (1) does not follow from an underlying higgsed E8 gauge group (2) leaves the class of theories that can be analyzed with current splitspectral cover techniques. This avoids recently proposed nogo theorems for models with hypercharge flux, as required to break the GUT group. The appearance of additional fields is related geometrically to considering a more general class of sections and 4–1 splits. We show explicitly that the fourdimensional chiral matter index can still be computed using threedimensional oneloop ChernSimons terms.
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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Cited by 22 (2 self)
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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.
Physics of Ftheory compactifications without section [1406.5180
"... Abstract: We study the physics of Ftheory compactifications on genusone fibrations without section by using an Mtheory dual description. The fivedimensional action obtained by considering Mtheory on a CalabiYau threefold is compared with a sixdimensional Ftheory effective action reduced on ..."
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Abstract: We study the physics of Ftheory compactifications on genusone fibrations without section by using an Mtheory dual description. The fivedimensional action obtained by considering Mtheory on a CalabiYau threefold is compared with a sixdimensional Ftheory effective action reduced on an additional circle. We propose that the sixdimensional effective action of these setups admits geometrically massive U(1) vectors with a charged hypermultiplet spectrum. The absence of a section induces NSNS and RR threeform fluxes in Ftheory that are nontrivially supported along the circle and induce a shiftgauging of certain axions with respect to the KaluzaKlein vector. In the fivedimensional effective theory the KaluzaKlein vector and the massive U(1)s combine into a linear combination that is massless. This U(1) is identified with the massless U(1) corresponding to the multisection of the CalabiYau threefold in Mtheory. We confirm this interpretation by computing the oneloop ChernSimons terms for the massless vectors of the fivedimensional setup by integrating out all massive states. A closed formula is found that accounts for the hypermultiplets charged under the massive U(1)s. ar X iv
SU(5) Tops with Multiple U(1)s in Ftheory
"... We study Ftheory compactifications with up to two Abelian gauge group factors that are based on elliptically fibered CalabiYau 4folds describable as generic hypersurfaces. Special emphasis is put on elliptic fibrations based on generic Bl2P2[3]fibrations. These exhibit a MordellWeil group of ra ..."
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We study Ftheory compactifications with up to two Abelian gauge group factors that are based on elliptically fibered CalabiYau 4folds describable as generic hypersurfaces. Special emphasis is put on elliptic fibrations based on generic Bl2P2[3]fibrations. These exhibit a MordellWeil group of rank two corresponding to two extra rational sections which give rise to two Abelian gauge group factors. We show that an alternative description of the same geometry as a complete intersection makes the existence of a holomorphic zerosection manifest, on the basis of which we compute the U(1) generators and a class of gauge fluxes. We analyse the fibre degenerations responsible for the appearance of localised charged matter states, whose charges, interactions and chiral index we compute geometrically. We implement an additional SU(5) gauge group by constructing the four inequivalent toric tops giving rise to SU(5) × U(1) × U(1) gauge symmetry and analyse the matter content. We demonstrate that notorious nonflat points can be avoided in welldefined CalabiYau 4folds. These methods are applied to the remaining possible hypersurface fibrations with one generic Abelian gauge factor. We analyse the local limit of our SU(5) × U(1) × U(1) models and show that one of our models is not embeddable into E8 due to recombination of matter curves that cannot be described as a Higgsing of E8. We argue that such recombination forms a general mechanism that opens up new model building possibilities in Ftheory. We dedicate this work to Matthis Florian. ar X iv
Landscaping with fluxes and the E8 Yukawa Point in Ftheory
, 2014
"... Integrality in the Hodge theory of CalabiYau fourfolds is essential to find the vacuum structure and the anomaly cancellation mechanism of four dimensional Ftheory compactifications. We use the GriffithsFrobenius geometry and homological mirror symmetry to fix the integral monodromy basis in the ..."
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Cited by 3 (0 self)
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Integrality in the Hodge theory of CalabiYau fourfolds is essential to find the vacuum structure and the anomaly cancellation mechanism of four dimensional Ftheory compactifications. We use the GriffithsFrobenius geometry and homological mirror symmetry to fix the integral monodromy basis in the primitive horizontal subspace of CalabiYau fourfolds. The Gamma class and supersymmetric localization calculations in the 2d gauged linear sigma model on the hemisphere are used to check and extend this method. The result allows us to study the superpotential and the WeilPetersson metric and an associated tt* structure over the full complex moduli space of compact fourfolds for the first time. We show that integral fluxes can drive the theory to N=1 supersymmetric vacua at orbifold points and argue that fluxes can be chosen that fix the complex moduli of Ftheory compactifications at gauge enhancements including such with U(1) factors. Given the mechanism it is natural to start with the most generic complex structure families of elliptic CalabiYau 4fold fibrations over a given base. We classify these families in toric ambient spaces and among them the ones with heterotic duals. The method also applies to the creating of matter and Yukawa structures in Ftheory. We construct two SU(5) models in Ftheory with a Yukawa point that have a point on the base with an E8type singularity on the fiber and explore their embeddings in the global models. The explicit resolution of the singularity introduce a higher dimensional fiber and leads to novel features.
Ftheory on GenusOne Fibrations
"... We argue that Mtheory compactified on an arbitrary genusone fibration, that is, an elliptic fibration which need not have a section, always has an Ftheory limit when the area of the genusone fiber approaches zero. Such genusone fibrations can be easily constructed as toric hypersurfaces, and va ..."
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We argue that Mtheory compactified on an arbitrary genusone fibration, that is, an elliptic fibration which need not have a section, always has an Ftheory limit when the area of the genusone fiber approaches zero. Such genusone fibrations can be easily constructed as toric hypersurfaces, and various SU(5) × U(1)n and E6 models are presented as examples. To each genusone fibration one can associate a τfunction on the base as well as an SL(2,Z) representation which together define the IIB axiodilaton and 7brane content of the theory. The set of genusone fibrations with the same τfunction and SL(2,Z) representation, known as the TateShafarevich group, supplies an important degree of freedom in the corresponding Ftheory model which has not been studied carefully until now. Sixdimensional anomaly cancellation as well as Witten’s zeromode count on wrapped branes both imply corrections to the usual Ftheory dictionary for some of these models. In particular, neutral hypermultiplets which are localized at codimensiontwo fibers can arise. (All previous known examples of localized hypermultiplets were charged under the gauge group of the theory.) Finally, in the absence of a section some novel monodromies of Kodaira fibers are allowed which lead to new breaking patterns of nonAbelian gauge groups.
Box Graphs and Singular Fibers
"... drm physics.ucsb.edu We determine the higher codimension fibers of elliptically fibered CalabiYau fourfolds with section by studying the threedimensional N = 2 supersymmetric gauge theory with matter which describes the low energy effective theory of Mtheory compactified on the associated Weierst ..."
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drm physics.ucsb.edu We determine the higher codimension fibers of elliptically fibered CalabiYau fourfolds with section by studying the threedimensional N = 2 supersymmetric gauge theory with matter which describes the low energy effective theory of Mtheory compactified on the associated Weierstrass model, a singular model of the fourfold. Each phase of the Coulomb branch of this theory corresponds to a particular resolution of the Weierstrass model, and we show that these have a concise description in terms of decorated box graphs based on the representation graph of the matter multiplets, or alternatively by a class of convex paths on said graph. Transitions between phases have a simple interpretation as “flopping ” of the path, and in the geometry correspond to actual flop transitions. This description of the phases enables us to enumerate and determine the entire network between them, with various matter representations for all reductive Lie groups. Furthermore, we observe that each network of phases carries the structure of a (quasi)minuscule representation of a specific Lie algebra. Interpreted from a geometric point of view, this analysis determines the generators of the cone of effective curves as well as the network of flop transitions between crepant resolutions of singular elliptic CalabiYau fourfolds. From the box graphs we determine all fiber types in codimensions two and three, and we find new, nonKodaira, fiber types for E6, E7 and E8. ar X iv
Discrete Gauge Symmetries by Higgsing in fourdimensional FTheory Compactifications
, 2014
"... We study Ftheory compactifications to four dimensions that exhibit discrete gauge symmetries. Geometrically these arise by deforming elliptic fibrations with two sections to a genusone fibration with a bisection. From a fourdimensional field theory perspective they are remnant symmetries from a ..."
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We study Ftheory compactifications to four dimensions that exhibit discrete gauge symmetries. Geometrically these arise by deforming elliptic fibrations with two sections to a genusone fibration with a bisection. From a fourdimensional field theory perspective they are remnant symmetries from a Higgsed U(1) gauge symmetry. We implement such symmetries in the presence of an additional SU(5) symmetry and associated matter fields, giving a geometric prescription for calculating the induced discrete charge for the matter curves and showing the absence of Yukawa couplings that are forbidden by this charge. We present a detailed map between the field theory and the geometry, including an identification of the Higgs field and the massless states before and after the Higgsing. Finally we show that the Higgsing of the U(1) induces a Gflux which precisely accounts for the change in the CalabiYau Euler number so as to leave the D3 tadpole invariant. ar X iv