Abstract
We study three-dimensional mathcal{N} = 2 Spin(7) gauge theories with NS spinorial matters and with Nf vectorial matters. The quantum Coulomb branch on the moduli space of vacua is one- or two-dimensional depending on the matter contents. For particular values of (Nf, NS ), we find s-confinement phases and derive exact superpotentials. The 3d dynamics of Spin(7) is connected to the 4d dynamics via KK-monopoles. Along the Higgs branch of the Spin(7) theories, we obtain 3d mathcal{N} = 2 G2 or SU(4) theories and some of them lead to new s-confinement phases. As a check of our analysis we compute superconformal indices for these theories.
Highlights
20 NS for these theories and derive exact superpotentials which govern the confined phases
We study three-dimensional N = 2 Spin(7) gauge theories with NS spinorial matters and with Nf vectorial matters
We focused on the s-confinement phases which appear for (Nf, NS) = (0, 5), (1, 4), (2, 3), (3, 2) and (4, 1)
Summary
We will define the (semi-)classical Coulomb branch coordinates which correspond to the monopoles with a magnetic charge gi = αi∗ · H, where αi is a simple root and αi∗. Where we used the gauge transformation and diagonalized the adjoint scalar into the Cartan part. In this notation, the weyl chamber is given by r. Speaking, the Coulomb branch operator includes the dual photon which is a dualized scalar from the U(1) photon We omitted it for simplicity since the dual photon dependence is restored. For the 3d N = 2 pure Spin(7) theory without matters, all the Coulomb branch operators Yi get two gaugino zero-modes.
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