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

Apr 28, 2023
28 pages
Published in:
  • Nucl.Phys.B 998 (2024) 116415
  • Published: Dec 10, 2023
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Abstract: (Elsevier B.V.)
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, F,k and F,k respectively, with charges k=1,,(Nc1)/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.
Note:
  • 28 pages
  • Wilson loop
  • color
  • quark
  • thermal
  • gluon
  • Polyakov loop
  • Jona-Lasinio-Nambu model
  • mean field approximation