Preprint typeset in JHEP style-HYPER VERSION Imperial / TP / 13 / AH / 03 Monopole operators and Hilbert series of Coulomb branches of 3 d N = 4 gauge theories
Preprint typeset in JHEP style-HYPER VERSION Imperial / TP / 13 / AH / 03 Monopole operators and Hilbert series of Coulomb branches of 3 d N = 4 gauge theories
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以 JHEP 风格预印排版 - HYPER VERSION Imperial / TP / 13 / AH / 03 单极子算子和 3 d N = 4 规范理论的库仑分支的希尔伯特级数
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发表时间：
2014
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通讯作者：
A. Zaffaroni
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作者：
S. Cremonesi;A. Hanany;A. Zaffaroni
本文解决了一个长期存在的问题，即在2+1维N = 4超共形场论的库仑分支上如何确定手征环和模空间（即作为代数簇）.以前的技术涉及模空间和/或镜像对称的度量的计算。这些方法仅限于足够小的模空间，具有足够的对称性，或足够小的规范理论的希格斯分支。我们介绍了库仑分支的希尔伯特级数的一个简单公式，它适用于任何好的或丑陋的三维N = 4规范理论。该公式计算了由经典算符修饰的正则算符，即剩余规范群的卡西米尔不变量，这些规范群没有被磁通破坏。我们将我们的公式应用于几类规范理论。沿着这条路，我们对镜像对称性进行了各种测试，成功地比较了镜像理论中库仑分支的希尔伯特级数和希格斯分支的希尔伯特级数。ar X iv：1 30 9. 26 57 v3 [ he pth ] 1 2 Ja n 20 14
This paper addresses a long standing problem to identify the chiral ring and moduli space (i.e. as an algebraic variety) on the Coulomb branch of anN = 4 superconformal field theory in 2+1 dimensions. Previous techniques involved a computation of the metric on the moduli space and/or mirror symmetry. These methods are limited to sufficiently small moduli spaces, with enough symmetry, or to Higgs branches of sufficiently small gauge theories. We introduce a simple formula for the Hilbert series of the Coulomb branch, which applies to any good or ugly three-dimensional N = 4 gauge theory. The formula counts monopole operators which are dressed by classical operators, the Casimir invariants of the residual gauge group that is left unbroken by the magnetic flux. We apply our formula to several classes of gauge theories. Along the way we make various tests of mirror symmetry, successfully comparing the Hilbert series of the Coulomb branch with the Hilbert series of the Higgs branch of the mirror theory. ar X iv :1 30 9. 26 57 v3 [ he pth ] 1 2 Ja n 20 14