SQCD: A Geometric Apercu

By James Richard Andrew Gray, A. Hanany, Yang-Hui He, Vishnu Jejjala, Noppadol Mekareeya. 2008

160 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/287db04c169ba53d8c48f4de17331de516ca3401

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Citations in the corpus

The Hilbert series of the one instanton moduli space (2010, background): “12) of [32]: (∗B)B̃ = ∗(Mc) , M · ∗B = M · ∗B̃ = 0 .”
Hilbert Series for Constructing Lagrangians: expanding the phenomenologist's toolbox (2015, background): “6) is an example of a plethystic exponential [7, 9, 10, 13, 21], a generating function of all symmetric combinations of its argument (see A.”
Hilbert series and operator bases with derivatives in effective field theories (2015, methodology): “We note that the application of Molien’s formula to SU(2) invariants has also been treated in [5].”
Gauge Theories and Macdonald Polynomials (2011, background): “A relation of a similar limit of the N = 1 index with the counting problems discussed in [39, 40] was mentioned in [21].”
Low-derivative operators of the Standard Model effective field theory via Hilbert series methods (2015, background): “oups of a generating function known as the 1Provided the ﬁelds transform linearly under the symmetries of the theory, and the symmetry groups are compact Lie groups. – 2 – plethystic exponential (PE) [4, 6, 7, 10, 18]. The input to the PE is the ﬁeld content of the theory, meaning the number of ﬂavo”
2, 84, 30, 993, 560, 15456, 11962, 261485, . . .: higher dimension operators in the SM EFT (2015, unknown): “, the physics paper [42]”
Elliptic Hypergeometry of Supersymmetric Dualities (2009, background): “Counting of the gauge invariant operators for a number of supersymmetric gauge theories was considered in detail in [34, 39].”