标题： Z 极值化在类似手征的 Chern Simons 理论中 显示英文标题

标题： Z Extremization in Chiral-Like Chern Simons Theories

摘要： 我们研究了三维N=2 Chern-Simons物质理论在弱耦合下的局域自由能。 我们以三种不同的方式计算了两环R电荷，即通过标准微扰方法、通过在有限N下极化局域化分区函数以及通过应用大N的标准鞍点近似。我们表明，当考虑手征理论时，后一种方法无法得到预期的结果。 我们通过在自由能中恢复特征值的反射对称性来克服这些问题。 由于这种对称化，我们发现所采用的三种方法是一致的。 特别是，我们匹配了一个模型的计算，该模型的四维父理论是描述D3膜探测Hirzebruch曲面的箭头规范理论。 最后，我们对我们的结果的应用以及强耦合区域进行评论。 显示英文摘要

摘要： We study the localized free energy on S^3 of three-dimensional N=2 Chern-Simons matter theories at weak coupling. We compute the two loop R charge in three different ways, namely by the standard perturbative approach, by extremizing the localized partition function at finite N and by applying the standard saddle point approximation for large N. We show that the latter approach does not reproduce the expected result when chiral theories are considered. We circumvent these problems by restoring a reflection symmetry on the eigenvalues in the free energy. Thanks to this symmetrization we find that the three methods employed agree. In particular we match the computation for a model whose four dimensional parent is the quiver gauge theory describing D3 branes probing the Hirzebruch surface. We conclude by commenting on the application of our results and to the strong coupling regime.