Mirror symmetry and exact solution of 4D $N = 2$ gauge theories: I
Mirror symmetry and exact solution of 4D $N = 2$ gauge theories: I
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DOI：
10.4310/atmp.1997.v1.n1.a2
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发表时间：
1997-06
影响因子：
1.5
通讯作者：
S. Katz;P. Mayr;C. Vafa
中科院分区：
文献类型：
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作者：
S. Katz;P. Mayr;C. Vafa
利用几何工程在II型弦的背景下，我们得到了四维所有N=2规范理论的库仑支模空间的精确解，其中包括所选对具有任意多个双基本物的SU规范群的乘积，以及每个因子的任意多个基本物的乘积。渐近自由将可能性限制在具有根据ADE或仿射ADE动态图选择的双基本物质的SU群。许多结果可以利用K3的自镜性质以一种初等的方式得到。我们发现在某些情况下，N=2规范理论的库仑分支的解是以三维复流形而不是黎曼曲面的形式给出的。我们还研究了高维无张力弦理论的紧致化所产生的新的强耦合不动点，并考虑了它在三维N=4理论中的应用。
Using geometric engineering in the context of type II strings, we obtain exact solutions for the moduli space of the Coulomb branch of all N=2 gauge theories in four dimensions involving products of SU gauge groups with arbitrary number of bi-fundamental matter for chosen pairs, as well as an arbitrary number of fundamental matter for each factor. Asymptotic freedom restricts the possibilities to SU groups with bi-fundamental matter chosen according to ADE or affine ADE Dynkin diagrams. Many of the results can be derived in an elementary way using the self-mirror property of K3. We find that in certain cases the solution of the Coulomb branch for N=2 gauge theories is given in terms of a three dimensional complex manifold rather than a Riemann surface. We also study new stringy strong coupling fixed points arising from the compactification of higher dimensional theories with tensionless strings and consider applications to three dimensional N=4 theories.