Seiberg-Witten curves with O7±-planes

Abstract

Abstract We construct Seiberg-Witten curves for 5d $$ \mathcal{N} $$ N = 1 gauge theories whose Type IIB 5-brane configuration involves an O7-plane and discuss an intriguing relation between theories with an O7+-plane and those with an O7−-plane and 8 D7-branes. We claim that 5-brane configurations with an O7+-plane can be effectively understood as 5-brane configurations with a set of an O7−-plane and eight D7-branes with some special tuning of their masses such that the D7-branes are frozen at the O7−-plane. We check this equivalence between SU(N) gauge theory with a symmetric hypermultiplet and SU(N) gauge theory with an antisymmetric with 8 fundamentals, and also between SO(2N) gauge theory and Sp(N) gauge theory with eight fundamentals. We also compute the Seiberg-Witten curves for non-Lagrangian theories with a symmetric hypermultiplet, which includes the local ℙ2 theory with an adjoint.