Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2007-05-18
JHEP 0711:092,2007
Physics
High Energy Physics
High Energy Physics - Theory
75 pages, 22 figures
Scientific paper
10.1088/1126-6708/2007/11/092
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.
Butti Agostino
Forcella Davide
Hanany Amihay
Vegh David
Zaffaroni Alberto
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