Ring relations and mirror map from branes
Ring relations and mirror map from branes
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环关系和膜的镜像图
DOI：
10.1007/jhep03(2017)152
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发表时间：
2017
影响因子：
5.4
通讯作者：
Benjamin Assel
中科院分区：
文献类型：
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作者：
Benjamin Assel
本文研究了三维N $$ \mathcal{N} $$ = 4理论的真空空间，在IIB型膜上实现了该理论，并通过在适当的膜设置下积分出光模式得到了路径积分中的局部手性算子的插入。我们大部分的分析都集中在阿贝尔颤振理论上，它可以被实现为D3-D5-NS5膜阵列的低能理论。它们的真空空间包含一个希格斯分支（由半bps介子算子的v参数化）和一个库仑分支（由半bps单极子算子的v参数化）。我们证明了希格斯算符通过在理论的初始膜设置中添加F1弦和D3膜来插入，而库仑算符通过在特定方向上添加D1弦和D3膜来插入。这种方法有两个主要优点。首先，描述希格斯和库仑分支的环关系可以通过观察具有多种算子插入解释的特定膜设置来推导。这为库仑分支量子关系提供了一个新的推导。其次，镜像对偶理论的希格斯算子和库仑算子之间的映射可以从IIB s -对偶中以一种平凡的方式推导出来。
A bstractWe study the space of vacua of three-dimensional N$$ \mathcal{N} $$ = 4 theories from a novel approach building on the type IIB brane realization of the theory and in which the insertion of local chiral operators in the path integral is obtained from integrating out light modes in appropriate brane setups. Most of our analysis focuses on abelian quiver theories which can be realized as the low-energy theory of D3-D5-NS5 brane arrays. Their space of vacua contains a Higgs branch, parametrized by the vevs of half-BPS meson operators, and a Coulomb branch, parametrized by the vevs of half-BPS monopole operators. We show that the Higgs operators are inserted by adding F1 strings and D3 branes, while Coulomb operators are inserted by adding D1 strings and D3 branes, with specific orientations, to the initial brane setup of the theory. This approach has two main advantages. First the ring relations describing the Higgs and Coulomb branches can be derived by looking at specific brane setups with multiple interpretations in terms of operator insertions. This provides a new derivation of the Coulomb branch quantum relations. Secondly the map between the Higgs and Coulomb operators of mirror dual theories can be derived in a trivial way from IIB S-duality.