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外文期刊>The journal of high energy physics
>Boundaries and defects of $$ mathcal{N}=4 $$ SYM with 4 supercharges. Part II: Brane constructions and 3 d$$ mathcal{N}=2 $$ field theories
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Boundaries and defects of $$ mathcal{N}=4 $$ SYM with 4 supercharges. Part II: Brane constructions and 3 d$$ mathcal{N}=2 $$ field theories
A bstract We study the vacuum moduli spaces of 3 d N = 2 $$ mathcal{N}=2 $$ supersymmetric quantum field theories by applying the formalism developed in our previous paper [1]. The 3 d theories can be realized by branes in type IIB string theory, which in a decoupling limit reduce to 4 d N = 4 $$ mathcal{N}=4 $$ super-Yang-Mills theory on an interval with BPS defects inserted. The moduli space of a given 3 d theory is obtained by solving a generalization of Nahm’s equations with appropriate boundary/junction conditions, along with help from the S-duality of type IIB string theory. Our classical computations reproduce many known results about the quantum-corrected moduli spaces of 3 d theories, e.g. U( N ~( c )) theories with N ~( f )flavors with mass and FI parameters turned on. In particular, our methods give first-principles derivations of several results in the literature, including the s -rule, quantum splitting of classical Coulomb branches, the lifting of the Coulomb branch by non-Abelian instantons, quantum merging of Coulomb and Higgs branches, and phase transitions from re-ordering 5-branes.
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机译：Bstract我们研究了3 d n = 2 $$$ mathcal {n} = 2 $$超对对称量子域理论的真空模数通过应用我们之前的论文中发育的形式主义[1]。在IIB型串理论中的布兰斯可以实现3天理论，该钢筋理论中的结转限制减少到4 d n = 4 $$$ mathcal {n} = 4 $$超级杨磨坊理论与BPS缺陷的间隔插入。通过求解具有适当的边界/结条件的NaHM等式的概括，以及来自IIB型串串理论的S-二元的帮助来获得给定的3d理论的模态空间。我们的古典计算再现了许多关于3 D理论的量子校正模态空间的已知结果，例如， U（n〜（c））与质量和FI参数的N〜（f）味道的理论打开。特别地，我们的方法给出了文献中的几个结果的第一原理推导，包括S-Rule，量子分裂的古典库仑分支，通过非阿比越乐园提升库仑分支，库仑和希格斯分支的量子合并，从重新订购5-Branes的相位过渡。
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