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FTheory and the MordellWeil Group of EllipticallyFibered CalabiYau Threefolds
 JHEP 1210 (2012) 128 [arXiv:1208.2695 [hepth
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Anomaly Cancellation And Abelian Gauge Symmetries
 In Ftheory, JHEP 1302
, 2013
"... cvetic at cvetic.hep.upenn.edu, grimm at mpp.mpg.de, klevers at sas.upenn.edu We study 4D Ftheory compactifications on singular CalabiYau fourfolds with fluxes. The resulting N = 1 effective theories can admit nonAbelian and U(1) gauge groups as well as charged chiral matter. In these setups we a ..."
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Cited by 33 (9 self)
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cvetic at cvetic.hep.upenn.edu, grimm at mpp.mpg.de, klevers at sas.upenn.edu We study 4D Ftheory compactifications on singular CalabiYau fourfolds with fluxes. The resulting N = 1 effective theories can admit nonAbelian and U(1) gauge groups as well as charged chiral matter. In these setups we analyze anomaly cancellation and the generalized GreenSchwarz mechanism. This requires the study of 3D N = 2 theories obtained by a circle compactification and their Mtheory duals. Reducing Mtheory on resolved CalabiYau fourfolds corresponds to considering the effective theory on the 3D Coulomb branch in which certain massive states are integrated out. Both 4D gaugings and 3D oneloop corrections of these massive states induce ChernSimons terms. All 4D anomalies are captured by the oneloop terms. The ones corresponding to the mixed gaugegravitational anomalies depend on the KaluzaKlein vector and are induced by integrating out KaluzaKlein modes of the U(1) charged matter. In Mtheory all ChernSimons terms classically arise from G4flux. We find that Ftheory fluxes implement automatically the 4D GreenSchwarz mechanism if nontrivial geometric relations for the resolved CalabiYau fourfold are satisfied. We confirm these relations in various explicit examples and elucidate the general construction of U(1) symmetries in Ftheory. We also compare anomaly cancellation in Ftheory with its analog in Type IIB orientifold setups.
FTheory Compactifications with Multiple U(1)Factors: Constructing Elliptic Fibrations with Rational Sections
, 2013
"... We study Ftheory compactifications with U(1)×U(1) gauge symmetry on elliptically fibered CalabiYau manifolds with a rank two MordellWeil group. We find that the natural presentation of an elliptic curve E with two rational points and a zero point is the generic CalabiYau onefold in dP2. We dete ..."
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Cited by 30 (4 self)
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We study Ftheory compactifications with U(1)×U(1) gauge symmetry on elliptically fibered CalabiYau manifolds with a rank two MordellWeil group. We find that the natural presentation of an elliptic curve E with two rational points and a zero point is the generic CalabiYau onefold in dP2. We determine the birational map to its Tate and Weierstrass form and the coordinates of the two rational points in Weierstrass form. We discuss its resolved elliptic fibrations over a general base B and classify them in the case of B = P2. A thorough analysis of the generic codimension two singularities of these elliptic CalabiYau manifolds is presented. This determines the general U(1)×U(1)charges of matter in corresponding Ftheory compactifications. The matter multiplicities for the fibration over P2 are determined explicitly and shown to be consistent with anomaly cancellation. Explicit toric examples are constructed, both with U(1)×U(1) and SU(5)×U(1)×U(1) gauge symmetry. As a byproduct, we prove the birational equivalence of the two elliptic fibrations with elliptic fibers in the two blowups Bl(1,0,0)P²(1, 2, 3) and Bl(0,1,0)P2(1, 1, 2) employing birational maps and extremal transitions.
Superconformal Partition Functions and Nonperturbative Topological Strings
, 2013
"... We propose a nonperturbative definition for refined topological strings. This can be used to compute the partition function of superconformal theories in 5 dimensions on squashed S5 and the superconformal index of a large number of 6 dimensional (2, 0) and (1, 0) theories, including that of N coinc ..."
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Cited by 26 (4 self)
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We propose a nonperturbative definition for refined topological strings. This can be used to compute the partition function of superconformal theories in 5 dimensions on squashed S5 and the superconformal index of a large number of 6 dimensional (2, 0) and (1, 0) theories, including that of N coincident M5 branes. The result can be expressed as an integral over the product of three combinations of topological string amplitudes. SL(3,Z) modular transformations acting by inverting the coupling constants of the refined topological string play a key role.
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.
Effective action of 6D FTheory with U(1) factors: Rational sections make ChernSimons terms jump,” JHEP 1307
, 2013
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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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Cited by 5 (1 self)
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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