Abstract
Supersymmetric Sp(k) quantum chromodynamics with 8 supercharges in space-time dimensions 3 to 6 can be realised by two different Type II brane configurations in the presence of orientifolds. Consequently, two types of magnetic quivers describe the Higgs branch of the Sp(k) SQCD theory. This is a salient example of a general phenomenon: a given hyper-Kähler Higgs branch may admit several magnetic quiver constructions. It is then natural to wonder if these different magnetic quivers, which are described by 3d mathcal{N} = 4 theories, are dual theories. In this work, the unitary and orthosymplectic magnetic quiver theories are subjected to a variety of tests, providing evidence that they are IR dual to each other. For this, sphere partition function and supersymmetric indices are compared. Also, we study half BPS line defects and find interesting regularities from the viewpoints of exact results, brane configurations, and 1-form symmetry.
Highlights
A long-standing challenge in quantum field theory is a strongly coupled phase, due to the breakdown of conventional techniques
At the end of the section, we demonstrate the identification of some 0-form symmetries, including that from gauging the 1-form symmetry, in the two types of magnetic quivers
A Wilson line at an Sp gauge node is dual to a Wilson line at the corresponding unitary gauge node from the left in the quiver diagrams. (Observation 1, 3.) Note that a Wilson line at the middle Sp gauge node corresponds to a direct sum of those at the two spinor nodes. (Observation 5.) On the other hand, a Wilson line at a non-abelian SO gauge node is dual to a direct sum of one(s) at the corresponding unitary gauge node(s) and one at the left U(1) node. (Observation 2, 4, 6.) As a result, it is consistent with the guiding principle so that the total dimensions of representations are equal
Summary
A long-standing challenge in quantum field theory is a strongly coupled phase, due to the breakdown of conventional techniques. Not all properties of the IR SCFT may be apparent in the UV description This is famously known for the orthosymplectic mirror quiver, which lacks FI parameters such that the Coulomb branch global symmetry is not manifest. In view of the exact partition functions (iii), (v)–(vii), only some are sensitive to the global structure of the gauge group in the UV description This happens when the precise choice of magnetic lattice or cocharacter lattice is involved; for instance, in the monopole formula, the superconformal index, and the A-twisted index. Like the sphere partition function or the Higgs branch Hilbert series, are only sensitive to the Lie algebra of the underlying gauge group. This paper provides a detailed study of the IR duality between unitary and orthosymplectic magnetic quivers by exact partition functions (v)–(vii), including line defects (viii). Computational results on partition functions are provided in appendix B for the superconformal index, in appendix C for twisted indices, and in appendix D for the sphere partition function
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