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Toric bases for 6D F-theory models. (English) Zbl 1255.81210
Summary: 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 \(\mathfrak e_8, \mathfrak f_4\), and \(\mathfrak g_2 \oplus \mathfrak {su}(2)\) with minimal (non-Higgsable) matter.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
83F05 Cosmology
83E30 String and superstring theories in gravitational theory
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
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