We analyze nonperturbative corrections to the superpotential of seven-brane gauge theories on type IIB and $F$-theory warped Calabi-Yau compactifications. We show, in particular, that such corrections modify the holomorphic Yukawa couplings by an exponentially suppressed contribution, generically solving the Yukawa rank-one problem of certain $F$-theory local models. We provide explicit expressions for the nonperturbative correction to the seven-brane superpotential, and check that it is related to a noncommutative deformation to the tree-level superpotential via a Seiberg-Witten map.

• Received 8 January 2010

DOI:https://doi.org/10.1103/PhysRevLett.104.231601