Towards Deconstruction of the Type D (2,0) Theory

TL;DR

This paper introduces a 4d supersymmetric theory that deconstructs the 6d (2,0) D_k theory, using a necklace quiver with alternating gauge groups, and validates it through index and Hilbert series comparisons.

Contribution

It proposes a novel 4d deconstruction of the 6d (2,0) D_k theory and addresses technical challenges in Hilbert series calculations and gauge group choices.

Findings

Matching of 6d half-BPS index with 4d Higgs branch Hilbert series

Successful comparison with Coulomb branch formula in 3d reduction

Overcoming technical difficulties in non-complete intersection Hilbert series calculations

Abstract

We propose a four-dimensional supersymmetric theory that deconstructs, in a particular limit, the six-dimensional $(2,0)$ theory of type $D_k$. This 4d theory is defined by a necklace quiver with alternating gauge nodes $\mathrm{O}(2k)$ and $\mathrm{Sp}(k)$. 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 $\mathrm{O}$ versus $\mathrm{SO}$ gauge groups. Consistently, the result matches the Coulomb branch formula for the mirror theory upon reduction to 3d.