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 Kahler 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 N of D-branes. Explicit formulae are given for few examples, including C-3/Z(3), F-0, and dP(1).
Butti, A., Forcella, D., Hanany, A., Vegh, D., Zaffaroni, A. (2007). Counting chiral operators in quiver gauge theories. JOURNAL OF HIGH ENERGY PHYSICS, 2007(11), 092 [10.1088/1126-6708/2007/11/092].
Counting chiral operators in quiver gauge theories
ZAFFARONI, ALBERTO
2007
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 Kahler 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 N of D-branes. Explicit formulae are given for few examples, including C-3/Z(3), F-0, and dP(1).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.