Abstract
We propose a four-dimensional supersymmetric theory that deconstructs, in a particular limit, the six-dimensional (2, 0) theory of type Dk. This 4d theory is defined by a necklace quiver with alternating gauge nodes O(2k) and Sp(k). We test this proposal by comparing the 6d half-BPS index to the Higgs branch Hilbert series of the 4d theory. In the process, we overcome several technical difficulties, such as Hilbert series calculations for non-complete intersections, and the choice of O versus SO gauge groups. Consistently, the result matches the Coulomb branch formula for the mirror theory upon reduction to 3d.
Highlights
(MSYM) in 5d with gauge algebra A and D respectively [3, 4]
With the deconstruction of the type Dk N = (2, 0) theory in mind, we explore in the rest of this section the Coulomb branch Hilbert series of theories AGN for G an orthogonal or a symplectic group, and use these results as a guide for finding the correct mirror theory, which will be of type BGN1,G2 withorthogonal and symplectic gauge groups
Because of the data of table 3, we expect the mirror theory to be a circular quiver with gauge algebras Bk and Ck. We can check this against a Higgs branch Hilbert series. It appears that it is not possible to determine using this method if the gauge group of type Bk is SO(2k + 1) or O(2k + 1), as remarkably, both theories turn out to have the same Higgs branch Hilbert series, which is equal to the Coulomb branch Hilbert series of ASNp(k)
Summary
The Higgs branch of theories with eight supercharges is independent of the dimension of the theory (4d or 3d) [12], so we can as well compute it for the theory obtained from the IIA set-up by reducing along x3 This is implemented by T-duality, obtaining a IIB configuration with k D3 branes along (x1, x2, x6) and N NS5 branes along (x1, x2, x3, x4, x5). In addition we will need the “magnetic theories” to those These are generically a 3d theory with gauge group G, one adjoint hypermultiplet and N matter fields. Note that in the case when G is symplectic/(special) orthogonal, the matter fields will be half-hypermultiplets
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