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).
Articolo in rivista - Articolo scientifico
AdS-CFT correspondence; gauge-gravity correspondence
English
2007
2007
11
092
none
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].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/1136
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