On the 6d origin of discrete additional data of 4d gauge theories
On the 6d origin of discrete additional data of 4d gauge theories
复制标题
论4维规范理论离散附加数据的6维起源
DOI：
10.1007/jhep05(2014)020
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发表时间：
2013
影响因子：
5.4
通讯作者：
Yuji Tachikawa
中科院分区：
文献类型：
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作者：
Yuji Tachikawa
从规范代数的选择开始，四维规范理论的规范化涉及到额外的数据，即规范群和离散θ角。等价地，需要指定允许的线运算符的电荷集合。在本文中，我们研究如何在6d中表示这些额外的数据，当所讨论的4d理论是$ \mathcal{N} $ = 4超级杨米尔斯理论或$ \mathcal{N} $ = 2类S理论。我们将看到所谓TN理论的N-N对称性起着重要作用，作为副产品，我们将发现S类理论的超共形指数可以被精化，从而可以给出2d q-变形的杨-米尔斯理论，不同的规范群与同一规范代数相关联。
A bstractStarting with a choice of gauge algebras, specification of a 4d gauge theory involves additional data, namely the gauge groups and the discrete theta angles. Equivalently, one needs to specify the set of charges of allowed line operators. In this note, we study how these additional data are represented in 6d, when the 4d theory in question is an $ \mathcal{N} $ = 4 super Yang-Mills theory or an $ \mathcal{N} $ = 2 class S theory. We will see that the ℤN symmetry of the so-called TN theory plays an important role.As a byproduct, we will find that the superconformal index of class S theories can be refined so that it can give 2d q-deformed Yang-Mills theory with different gauge groups associated to the same gauge algebra.