F-theory compactifications with multiple U(1)-factors: constructing elliptic fibrations with rational sections View Full Text


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Article Info

DATE

2013-06

AUTHORS

Mirjam Cvetič, Denis Klevers, Hernan Piragua

ABSTRACT

We 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 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 = 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 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)2(1, 2, 3) and Bl(0,1,0)2(1, 1, 2) employing birational maps and extremal transitions. More... »

PAGES

67

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    http://scigraph.springernature.com/pub.10.1007/jhep06(2013)067

    DOI

    http://dx.doi.org/10.1007/jhep06(2013)067

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    https://app.dimensions.ai/details/publication/pub.1014002142


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    256 https://www.grid.ac/institutes/grid.8647.d schema:alternateName University of Maribor
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