12:30 pm 3rd Floor Atrium
Superpotentials from Singular Divisors.
Determining what non-perturbative effects contribute to scalar potentials coming from string theory is of crucial importance for studying string phenomenology. We identify novel contributions from Euclidean D3-branes wrapping singular divisors in Calabi-Yau orientifold compactifications of type IIB string theory. Witten’s criteria for non-perturbative superpotential corrections applies when the divisor is smooth, but we argue that effective divisors of Calabi-Yau threefolds typically have singularities along rational curves. We generalize the counting of fermion zero modes to such singular divisors by detailing compactifications in which the singularities can be unwound by passing through flop transitions. The examples that we present feature infinitely many isomorphic geometric phases, with corresponding infinitely generated effective cones. The resulting nonperturbative superpotentials are Jacobi theta functions, whose modular symmetries suggest the existence of strong-weak coupling dualities involving inversion of divisor volumes.