Higgs Branch , HyperKähler quotient and duality in SUSY N = 2 Yang – Mills theories
Higgs Branch , HyperKähler quotient and duality in SUSY N = 2 Yang – Mills theories
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希格斯支线、HyperKähler 商和 SUSY N = 2 Yang – Mills 理论中的对偶性
DOI：
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发表时间：
1996
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影响因子：
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通讯作者：
B. Pioline
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作者：
I. Antoniadis;B. Pioline
用超Kähler靶空间上的非线性四维σ模型描述了Higgs分支中N=2超对称场论的低能极限，该模型经典地由规范群得到了原始平坦超多重空间的超Kähler商.我们以教学的方式回顾了这一结构，并用不同的例子进行了说明，特别注意了低能量理论中出现的奇点。特别地，我们深入研究了具有Nf味的Seiberg-Witten SU(2)理论的Higgs支奇性，它被Witten解释为R上一个瞬子的模空间中的一个小瞬子奇点。通过显式地计算度规，我们证明了这个Higgs支与U(1)N=2SUSY理论的Higgs支相重合，其味的数目由Seiberg-Witten理论在库仑相中的奇点结构所预测。通过使用Biquard等人的几何解释，我们发现了Higgs相对偶的另一个例子，即U(NC)nF味的Higgs相与U(nF−nc)nF味理论之间的Higgs相。这种对偶性可能与理解Seiberg在N=1SUSYSU(Nc)规范理论中的猜想对偶性NC↔Nf−Nc有关。电子邮件：antoniad@oreee.Polytech.fr Pioline@oreee.Polytech e.fr，也是法国巴黎诺马尔高等研究院，巴黎国家研究中心UPR A.0014。
Low–energy limits of N=2 supersymmetric field theories in the Higgs branch are described in terms of a non–linear 4–dimensional σ– model on a hyperKähler target space, classically obtained as a hyperKähler quotient of the original flat hypermultiplet space by the gauge group. We review in a pedagogical way this construction, and illustrate it in various examples, with special attention given to the singularities emerging in the low–energy theory. In particular, we thoroughly study the Higgs branch singularity of Seiberg–Witten SU(2) theory with Nf flavors, interpreted by Witten as a small instanton singularity in the moduli space of one instanton on R. By explicitly evaluating the metric, we show that this Higgs branch coincides with the Higgs branch of a U(1) N=2 SUSY theory with the number of flavors predicted by the singularity structure of Seiberg–Witten’s theory in the Coulomb phase. We find another example of Higgs phase duality, namely between the Higgs phases of U(Nc) Nf flavors and U(Nf − Nc) Nf flavors theories, by using a geometric interpretation due to Biquard et al. This duality may be relevant for understanding Seiberg’s conjectured duality Nc ↔ Nf − Nc in N=1 SUSY SU(Nc) gauge theories. antoniad@orphee.polytechnique.fr pioline@orphee.polytechnique.fr, also at Ecole Normale Supérieure, Paris Laboratoire Propre du CNRS UPR A.0014.