Seiberg-Witten curves with O7±-planes

A bstract We construct Seiberg-Witten curves for 5d 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 (2 N) 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 ℙ 2 theory with an adjoint.