Counting Chiral Operators in Quiver Gauge Theories
Abstract
We discuss in detail the problem of counting BPS gauge invariant operators in the chiral ring of quiver gauge theories living on D-branes probing generic toric CY singularities. The computation of generating functions that include counting of baryonic operators is based on a relation between the baryonic charges in field theory and the Kaehler moduli of the CY singularities. A study of the interplay between gauge theory and geometry shows that given geometrical sectors appear more than once in the field theory, leading to a notion of "multiplicities". We explain in detail how to decompose the generating function for one D-brane into different sectors and how to compute their relevant multiplicities by introducing geometric and anomalous baryonic charges. The Plethystic Exponential remains a major tool for passing from one D-brane to arbitrary number of D-branes. Explicit formulae are given for few examples, including C^3/Z_3, F_0, and dP_1.
Keywords
Cite
@article{arxiv.0705.2771,
title = {Counting Chiral Operators in Quiver Gauge Theories},
author = {Agostino Butti and Davide Forcella and Amihay Hanany and David Vegh and Alberto Zaffaroni},
journal= {arXiv preprint arXiv:0705.2771},
year = {2009}
}
Comments
75 pages, 22 figures