Baryonic Generating Functions

Abstract

We show how it is possible to use the plethystic program in order to compute baryonic generating functions that count BPS operators in the chiral ring of quiver gauge theories living on the world volume of D branes probing a non compact CY manifold. Special attention is given to the conifold theory and the orbifold C^2/Z_2 times C, where exact expressions for generating functions are given in detail. This paper solves a long standing problem for the combinatorics of quiver gauge theories with baryonic moduli spaces. It opens the way to a statistical analysis of quiver theories on baryonic branches. Surprisingly, the baryonic charge turns out to be the quantized Kahler modulus of the geometry.

44 pages, 7 figures; fonts changed

References in corpus (10)

• Counting Gauge Invariants: the Plethystic Program
• Counting 1/8-BPS Dual-Giants
• Dual Giant Gravitons in Sasaki-Einstein Backgrounds
• Counting BPS Baryonic Operators in CFTs with Sasaki-Einstein duals
• Brane Tilings and Exceptional Collections
• Deformations of conformal theories and non-toric quiver gauge theories
• Deformations of Toric Singularities and Fractional Branes
• Dual giant gravitons in AdS${}_m$ $\times$ Y${}^n$ (Sasaki-Einstein)
• At the horizon of a supersymmetric AdS_5 black hole: Isometries and half-BPS giants
• Finite N Index and Angular Momentum Bound from Gravity

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