We present recent advances in constructions of globally consistent

F-theory compactifications with the exact chiral spectrum of the minimal

supersymmetric Standard Model. We highlight the first such example and

then turn to a subsequent systematic exploration of the landscape of

F-theory three-family Standard Models with a gauge coupling unification.

Employing algebraic geometry techniques, all global consistency

conditions of these models can be reduced to a single criterion on the

base of the underlying elliptically fibered Calabi-Yau fourfolds. For

toric bases, this criterion only depends on an associated polytope and

is satisfied for at least quadrillion bases, each of which defines a

distinct compactification. We conclude with pointing out important

outstanding issues.

# Globally Consistent Three-family Standard Models in F-theory

Mirjam Cvetic

University of Pennsylvania

April 29, 2019