论文标题
希格斯，库仑和霍尔·利特伍德
Higgs, Coulomb, and Hall-Littlewood
论文作者
论文摘要
可以通过Higgs分支的Hilbert系列分析4D $ \ MATHCAL {n} = 2 $ scfts的Higgs分支，或者在特殊情况下，可以通过计算Hall-Little Woodwood索引。对于任何对应于Riemann属表面的类$ \ Mathcal {S} $理论，它们被认为是相同的。我们介绍了几个反例的家庭。我们发现，对于任何类$ \ Mathcal {s} $理论，具有四个或多个$ \ mathbb {z} _2 $ twist-twist的穿刺，它们不匹配。我们为这些理论构建了3D镜子，并分析了他们的库仑分支希尔伯特系列，以计算Higgs Branch Hilbert系列4D理论。我们进一步在类$ \ Mathcal {s} $的类中构建$ a = c $理论，并使用扭曲的穿刺和这些理论（包括$ \ hat {d} _4（su（2n+1））$理论，具有与希格斯·希格斯（Higgs Higgs Branch）希尔伯特系列的Hall-littlewood Index不同。我们猜想所有$ a = c $带有非空的希格斯分支机构的情况都是这种情况，包括$ \ nathcal {n} \ ge 3 $ scfts。
The Higgs branch of 4d $\mathcal{N}=2$ SCFTs can be analyzed via the Hilbert series of the Higgs branch or, in special cases, by computing the Hall-Littlewood index. For any class $\mathcal{S}$ theory corresponding to a genus-zero Riemann surface, they are conjectured to be identical. We present several families of counterexamples. We find that for any class $\mathcal{S}$ theory with four or more $\mathbb{Z}_2$-twisted punctures, they do not match. We construct 3d mirrors for such theories and analyze their Coulomb branch Hilbert series to compute the Higgs branch Hilbert series of the 4d theory. We further construct $a=c$ theories in class $\mathcal{S}$ using the twisted punctures, and these theories, which includes the $\hat{D}_4(SU(2n+1))$ theories, have Hall--Littlewood index different from the Hilbert series of the Higgs branch. We conjecture that this is the case for all $a=c$ theories with non-empty Higgs branch, including $\mathcal{N}\ge 3$ SCFTs.
