SQCD: A Geometric Apercu

Details SQCD: A Geometric Apercu SQCD: A Geometric Apercu

2008-03-29

arxiv.org/abs/0803.4257v2

JHEP0805:099,2008

Physics

High Energy Physics

High Energy Physics - Theory

49 pages, 1 figure

Scientific paper

10.1088/1126-6708/2008/05/099

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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