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Journal of High Energy Physics Volume 2008 JHEP05(2008) Create an alert RSS this journal

James Gray et al JHEP05(2008)099 doi:10.1088/1126-6708/2008/05/099

SQCD: a geometric aperçu

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James Gray1, Yang-Hui He1,2,3, Amihay Hanany4, Noppadol Mekareeya4 and Vishnu Jejjala5

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Abstract References Cited By
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.

Keywords

Differential and Algebraic Geometry

Supersymmetric gauge theory

QCD

 

E-print Number: 0803.4257

Cited: by |

Refers: to

PACS

12.38.-t Quantum chromodynamics

11.30.Hv Flavor symmetries

11.30.Fs Global symmetries (e.g., baryon number, lepton number)

11.30.Rd Chiral symmetries

Subjects

Particle physics and field theory

Dates

Issue 05 (May 2008)

Received 7 April 2008, accepted for publication 12 May 2008

Published 28 May 2008



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