Quivers, words and fundamentals

Open Access
Regular Article - Theoretical Physics


A systematic study of holomorphic gauge invariant operators in general \( \mathcal{N} \) = 1 quiver gauge theories, with unitary gauge groups and bifundamental matter fields, was recently presented in [1]. For large ranks a simple counting formula in terms of an infinite product was given. We extend this study to quiver gauge theories with fundamental matter fields, deriving an infinite product form for the refined counting in these cases. The infinite products are found to be obtained from substitutions in a simple building block expressed in terms of the weighted adjacency matrix of the quiver. In the case without fundamentals, it is a determinant which itself is found to have a counting interpretation in terms of words formed from partially commuting letters associated with simple closed loops in the quiver. This is a new relation between counting problems in gauge theory and the Cartier-Foatamonoid. For finite ranks of the unitary gauge groups, the refined counting is given in terms of expressions involving Littlewood-Richardson coefficients.


Gauge Symmetry 1/N Expansion Global Symmetries AdS-CFT Correspondence 


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Copyright information

© The Author(s) 2015

Authors and Affiliations

  1. 1.Centre for Research in String Theory, School of Physics and AstronomyQueen Mary University of LondonLondonU.K.

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