Discrete gauging and Hasse diagrams

Abstract

We analyse the Higgs branch of 4d \mathcal{N}=2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mstyle mathvariant="script"> <mml:mi>𝒩</mml:mi> </mml:mstyle> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> </mml:mrow> </mml:math> SQCD gauge theories with non-connected gauge groups \widetilde{\mathrm{SU}}(N) = \mathrm{SU}(N) \rtimes_{I,II} \mathbb{Z}_2 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mover> <mml:mstyle mathvariant="normal"> <mml:mi>S</mml:mi> <mml:mi>U</mml:mi> </mml:mstyle> <mml:mo accent="true">̃</mml:mo> </mml:mover> <mml:mo stretchy="false" form="prefix">(</mml:mo> <mml:mi>N</mml:mi> <mml:mo stretchy="false" form="postfix">)</mml:mo> <mml:mo>=</mml:mo> <mml:mstyle mathvariant="normal"> <mml:mi>S</mml:mi> <mml:mi>U</mml:mi> </mml:mstyle> <mml:mo stretchy="false" form="prefix">(</mml:mo> <mml:mi>N</mml:mi> <mml:mo stretchy="false" form="postfix">)</mml:mo> <mml:msub> <mml:mo>⋊</mml:mo> <mml:mrow> <mml:mi>I</mml:mi> <mml:mo>,</mml:mo> <mml:mi>I</mml:mi> <mml:mi>I</mml:mi> </mml:mrow> </mml:msub> <mml:msub> <mml:mstyle mathvariant="double-struck"> <mml:mi>ℤ</mml:mi> </mml:mstyle> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> </mml:math> whose study was initiated in . We derive the Hasse diagrams corresponding to the Higgs mechanism using adapted characters for representations of non-connected groups. We propose 3d \mathcal{N}=4 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mstyle mathvariant="script"> <mml:mi>𝒩</mml:mi> </mml:mstyle> <mml:mo>=</mml:mo> <mml:mn>4</mml:mn> </mml:mrow> </mml:math> magnetic quivers for the Higgs branches in the type I <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mi>I</mml:mi> </mml:math> discrete gauging case, in the form of recently introduced wreathed quivers, and provide extensive checks by means of Coulomb branch Hilbert series computations.

Topics & Concepts