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34
MODELS OF PARTICLE PHYSICS FROM TYPE IIB STRING THEORY AND FTHEORY: A REVIEW
, 2012
"... We review particle physics model building in type IIB string theory and Ftheory. This is a region in the landscape where in principle many of the key ingredients required for a realistic model of particle physics can be combined successfully. We begin by reviewing moduli stabilisation within this f ..."
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Cited by 33 (4 self)
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We review particle physics model building in type IIB string theory and Ftheory. This is a region in the landscape where in principle many of the key ingredients required for a realistic model of particle physics can be combined successfully. We begin by reviewing moduli stabilisation within this framework and its implications for supersymmetry breaking. We then review model building tools and developments in the weakly coupled type IIB limit, for both local D3branes at singularities and global models of intersecting D7branes. Much of recent model building work has been in the strongly coupled regime of Ftheory due to the presence of exceptional symmetries which allow for the construction of phenomenologically appealing Grand Unified Theories. We review both local and global Ftheory model building starting from the fundamental concepts and tools regarding how the gauge group, matter sector and operators arise, and ranging to detailed phenomenological properties explored in the literature.
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.
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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Cited by 27 (5 self)
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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.
Geometric Engineering in Toric FTheory and GUTs with U(1) Gauge Factors
, 2011
"... An algorithm to systematically construct all CalabiYau elliptic fibrations realized as hypersurfaces in a toric ambient space for a given base and gauge group is described. This general method is applied to the particular question of constructing SU(5) GUTs with multiple U(1) gauge factors. The bas ..."
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Cited by 27 (3 self)
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An algorithm to systematically construct all CalabiYau elliptic fibrations realized as hypersurfaces in a toric ambient space for a given base and gauge group is described. This general method is applied to the particular question of constructing SU(5) GUTs with multiple U(1) gauge factors. The basic data consists of a top over each toric divisor in the base together with compactification data giving the embedding into a reflexive polytope. The allowed choices of compactification data are integral points in an auxiliary polytope. In order to ensure the existence of a lowenergy gauge theory, the elliptic fibration must be flat, which is reformulated into conditions on the top and its embedding. In particular, flatness of SU(5) fourfolds imposes additional linear constraints on the auxiliary polytope of compactifications, and is therefore nongeneric. Abelian gauge symmetries arising in toric Ftheory compactifications are studied systematically. Associated to each top, the toric MordellWeil group determining the minimal number of U(1) factors is computed. Furthermore, all SU(5)tops and their splitting types are determined and used to infer the pattern of U(1) matter charges.
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