Abstract
We consider 5d mathcal{N} = 1 Sp(1) gauge theory based on a brane configuration with an O5-plane. At the UV fixed point, the theory with no matter enjoys enhanced global symmetry SU(2) or U(1) depending on the discrete theta angle θ = 0, π (mod 2π). A naive brane configuration with an O5-plane, however, does not distinguish two different theories, as it describes the weak coupling region. We devise a technique for computing 5d Seiberg-Witten curve of the two theories from the brane web with an O5-plane. Their Seiberg-Witten curves show that their M5 configurations under the presence of OM5-planes are different. The decompactification limit of each Seiberg-Witten curve also shows distinct phase structures in their Coulomb branch leading to significantly different (p, q) 5-brane configurations with an O5-plane in the strong coupling region.
Highlights
Decompactification limit of 5d Seiberg-Witten curves of E1 and E1We have seen how the discrete theta angle of the 5d pure Sp(1) gauge theory is realized in terms of the Seiberg-Witten curves, which are the configurations of M5-branes under the existence of an OM5-plane
Symmetry enhancement can be seen from 7-branes attached to the external 5-branes [6]
In order to address this issue, we first move to the M-theory picture as follows: we consider the compactification of the 5-brane web diagram with an O5-plane on a circle
Summary
We have seen how the discrete theta angle of the 5d pure Sp(1) gauge theory is realized in terms of the Seiberg-Witten curves, which are the configurations of M5-branes under the existence of an OM5-plane. We will see how the difference with respect to the discrete theta angle appears in the original (p, q) 5-brane web with an O5-plane in type IIB string theory
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