Toric bases for 6D F-theory models

Authors

  • D.R. Morrison,

    1. Departments of Mathematics and Physics, University of California, Santa Barbara, Santa Barbara, CA 93106, USA
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  • W. Taylor

    Corresponding author
    1. Center for Theoretical Physics, Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
    • Center for Theoretical Physics, Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
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Abstract

We find all smooth toric bases that support elliptically fibered Calabi-Yau threefolds, using the intersection structure of the irreducible effective divisors on the base. These bases can be used for F-theory constructions of six-dimensional quantum supergravity theories. There are 61,539 distinct possible toric bases. The associated 6D supergravity theories have a number of tensor multiplets ranging from 0 to 193. For each base an explicit Weierstrass parameterization can be determined in terms of the toric data. The toric counting of parameters matches with the gravitational anomaly constraint on massless fields. For bases associated with theories having a large number of tensor multiplets, there is a large non-Higgsable gauge group containing multiple irreducible gauge group factors, particularly those having algebras ��8, ��4, and ��g2 ⊕ ����(2) with minimal (non-Higgsable) matter.

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