Counting Gauge Invariant Operators in SQCD with Classical Gauge Groups

Abstract

We use the plethystic programme and the Molien-Weyl fomula to compute generating functions, or Hilbert Series, which count gauge invariant operators in SQCD with the SO and Sp gauge groups. The character expansion technique indicates how the global symmetries are encoded in the generating functions. We obtain the full character expansion for each theory with arbitrary numbers of colours and flavours. We study the orientifold action on SQCD with the SU gauge group and examine how it gives rise to SQCD with the SO and Sp gauge groups. We establish that the classical moduli space of SQCD is not only irreducible, but is also an affine Calabi-Yau cone over a weighted projective variety.

34 pages, 2 figures, 4 tables

References in corpus (14)

• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• Counting Gauge Invariants: the Plethystic Program
• The Master Space of N=1 Gauge Theories
• SQCD: A Geometric Apercu
• Counting Chiral Operators in Quiver Gauge Theories
• Counting BPS operators in N=4 SYM
• STRINGVACUA: A Mathematica Package for Studying Vacuum Configurations in String Phenomenology
• Counting BPS Baryonic Operators in CFTs with Sasaki-Einstein duals
• Exploring the Vacuum Geometry of N=1 Gauge Theories
• Drinfeld second realization of the quantum affine superalgebras of $D^{(1)}(2,1;x)$ via the Weyl groupoid
• TASI-2002 Lectures: Non-perturbative Supersymmetry
• Typicality, Black Hole Microstates and Superconformal Field Theories
• BPS Partition Functions for Quiver Gauge Theories: Counting Fermionic Operators
• Plethystics and instantons on ALE spaces

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