Seiberg-Witten curves with O7${}^{\pm }$-planes

Abstract

We construct Seiberg-Witten curves for 5d $\mathcal{N}=1$ 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 ${\mathbb{P}}^2$ theory with an adjoint.

arXiv commentv1: 64 pages, 20 figures, v2: published version

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