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Building models of quarks and gluons with an arbitrary number of colors using Cartan-Polyakov loops

Authors: Renan CΓ’mara Pereira and Pedro Costa,

Ref.: Nucl. Phys. B 998, 116415-24 (2024)

Abstract: In this work we introduce the concept of Cartan-Polyakov loops, a special subset of Polyakov loops in the fundamental and antifundamental representation of the SU(𝑁𝑐) group, 𝓁_{F,π‘˜} and 𝓁_{F,π‘˜} respectively, with charges π‘˜ = 1, … , (𝑁𝑐 βˆ’ 1)βˆ•2. It constitutes a sufficient set of independent degrees of freedom and it is used to parametrize the thermal Wilson line. Polyakov loops not contained in this set are classified as non-Cartan-Polyakov loops. Using properties of the characteristic polynomial of the thermal Wilson line, we write a non-Cartan-Polyakov loop charge decomposition formula. This formalism allows one to readily build effective models of quarks and gluons with an arbitrary number of colors. We apply it to the Polyakov-Nambu-Jona-Lasinio model and to an effective glue model, in the mean field approximation, showing how to directly extend these models to higher values of 𝑁𝑐.

DOI: https://doi.org/10.1016/j.nuclphysb.2023.116415

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