F-theory compactifications with multiple U(1)-factors: constructing elliptic fibrations with rational sections
By M. Cvetič, Denis Klevers, Hernan Piragua. 2013
149 citations recorded by the source corpus.
A bstractWe study F-theory compactifications with U(1)×U(1) gauge symmetry on elliptically fibered Calabi-Yau manifolds with a rank two Mordell-Weil group. We find that the natural presentation of an elliptic curve $ \mathcal{E} $ with two rational points and a zero point is the generic Calabi-Yau onefold in dP2. We determine the birational map to its Tate and Weier- strass 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 = $ \mathbb{P} $2. A thorough analysis of the generic codimension two singularities of these elliptic Calabi-Yau manifolds is presented. This determines the general U(1)×U(1)-charges of matter in corresponding F-theory compactifications. The matter multiplicities for the fibration over $ \mathbb{P} $2 are determined explicitly and shown to be consistent with anomaly cancellation. Explicit toric examples are constructed, both with U(1)×U(1) and SU(5)×U(1)×U(1) gauge symmetry. As a by-product, we prove the birational equivalence of the two elliptic fibrations with elliptic fibers in the two blow-ups Bl(1,0,0)$ \mathbb{P} $2(1, 2, 3) and Bl(0,1,0)$ \mathbb{P} $2(1, 1, 2) employing birational maps and extremal transitions.
Subfields: Nuclear and High Energy Physics
View Paper: https://www.semanticscholar.org/paper/2ab8c8da51d3b23f1af5a93b38fed123c71b8ac5
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In Nuclear and High Energy Physics
- Min-xin Huang
- Thomas W. Grimm
- A. Klemm
- Denis Klevers
- Volker Braun
- Jan Keitel
- Maximilian Poretschkin
- Hernan Piragua
Citations in the corpus
- F-theory on all toric hypersurface fibrations and its Higgs branches (2014, methodology): “[35,39,42,77] for details), whereas π(Sm·Sn) and π(Sm·S0) are model-dependent.”
- Refined stable pair invariants for E-, M- and [p, q]-strings (2013, background): “These examples have been re-discovered and interesting variants that have three rational sections have been discussed in detail in [55, 56].”
- Geometric engineering in toric F-theory and GUTs with U(1) gauge factors (2013, background): “Studying global U(1) symmetries is a topic of intense current research [11, 12, 13, 14, 15, 16, 17, 18, 19].”