SQCD：一个几何模型
SQCD: A Geometric Apercu
摘要：
我们采取新的代数和几何的角度上的老问题SQCD。我们计数手征规范不变算子使用生成函数，或希尔伯特系列，来自plethystic程序和莫林-外尔公式。使用字符扩展技术，我们还看到如何在生成函数中编码全局对称性。配备这些方法和技术的算法代数几何，我们获得的字符扩展的理论与任意数量的颜色和味道。此外，计算代数几何允许我们系统地研究SQCD的经典真空模空间，并研究其不可约分量、度和合冲等结构。我们发现SQCD的真空流形是加权射影簇上的仿射Calabi-Yau锥。
英文摘要：
We take new algebraic and geometric perspectives on the old subject of SQCD. We count chiral gauge invariant operators using generating functions, or Hilbert series, derived from the plethystic programme and the Molien-Weyl formula. Using the character expansion technique, we also see how the global symmetries are encoded in the generating functions. Equipped with these methods and techniques of algorithmic algebraic geometry, we obtain the character expansions for theories with arbitrary numbers of colours and flavours. Moreover, computational algebraic geometry allows us to systematically study the classical vacuum moduli space of SQCD and investigate such structures as its irreducible components, degree and syzygies. We find the vacuum manifolds of SQCD to be affine Calabi-Yau cones over weighted projective varieties.
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