Matrix-model description of N=2 gauge theories with non-hyperelliptic Seiberg–Witten curves
Matrix-model description of N=2 gauge theories with non-hyperelliptic Seiberg–Witten curves
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具有非超椭圆 Seiberg-Witten 曲线的 N=2 规范理论的矩阵模型描述
DOI：
10.1016/j.nuclphysb.2003.09.028
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
N. Wyllard
中科院分区：
文献类型：
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作者：
S. Naculich;H. Schnitzer;N. Wyllard
利用矩阵模型方法研究了三种不同的N =2模型：物质在双基本表象中的U（N）×U（N）、物质在对称表象中的U（N）和物质在反对称表象中的U（N）.我们发现，（奇异）三次塞伯格-威滕曲线（和相关的塞伯格-威滕微分）所隐含的矩阵模型，虽然从以前提出的使用M-理论的不同形式，可以转化为后者，因此物理等价。我们还利用矩阵模型的微扰展开计算了规范耦合矩阵的单瞬子修正。对于具有对称或反对称物质的U（N）理论，我们使用我们论文中讨论的规范耦合矩阵的修改后的矩阵模型处方：来自矩阵模型的三次曲线和广义小西异常（hep-th/0303268）。此外，在具有反对称物质的U（N）理论的矩阵模型中，人们需要围绕一个与人们天真地预期的不同的真空膨胀。通过对矩阵模型公式的这些修改，本文的结果与Seiberg-Witten理论的M理论方法得到的结果完全一致。
Using matrix-model methods we study three different N =2 models: U(N)×U(N) with matter in the bifundamental representation, U(N) with matter in the symmetric representation, and U(N) with matter in the antisymmetric representation. We find that the (singular) cubic Seiberg–Witten curves (and associated Seiberg–Witten differentials) implied by the matrix models, although of a different form from the ones previously proposed using M-theory, can be transformed into the latter and are thus physically equivalent. We also calculate the one-instanton corrections to the gauge-coupling matrix using the perturbative expansion of the matrix model. For the U(N) theories with symmetric or antisymmetric matter we use the modified matrix-model prescription for the gauge-coupling matrix discussed in our paper: Cubic curves from matrix models and generalized Konishi anomalies (hep-th/0303268). Moreover, in the matrix model for the U(N) theory with antisymmetric matter, one is required to expand around a different vacuum than one would naively have anticipated. With these modifications of the matrix-model prescription, the results of this paper are in complete agreement with those of Seiberg–Witten theory obtained using M-theory methods.