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Quantum Yang-Mills charges in strongly coupled 2D lattice QCD with three flavors

Paulo A. Faria da Veiga1,*, Luiz A. Ferreira2,†, Henrique Malavazzi2,‡, and Ravi Mistry1,2,§

  • 1Instituto de Ciências Matemáticas e de Computação (ICMC), Universidade de São Paulo, P.O. Box 668, 13560-970 São Carlos, SP, Brasil
  • 2Instituto de Física de São Carlos (IFSC), Universidade de São Paulo, P.O. Box 369, 13560-970, São Carlos, SP, Brasil

  • *Contact author: veiga@icmc.usp.br
  • †Contact author: laf@ifsc.usp.br
  • ‡Contact author: henrique.malavazzi@usp.br
  • §Contact author: ravi.mistry.r@gmail.com
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Phys. Rev. D 113, 034508 – Published 24 February, 2026

DOI: https://doi.org/10.1103/cqqt-bf1w

Abstract

We investigate the quantum properties of the truly gauge-invariant and conserved charges of two-dimensional Yang-Mills theories, focusing on lattice QCD in the strong coupling regime. The construction of those charges uses the integral version of the (1+1)-dimensional Yang-Mills equations, and they correspond to the eigenvalues of a charge operator. The gauge invariance of the charges suggests that they are not confined, hence hadronic states may carry them. Using the path integral formalism with imaginary time (Euclidean), we evaluate the correlation functions of those charges on baryon and meson states through functional integrals over the gauge group SU(N) (N=2, 3) and Grassmannian variables—the fermionic fields. Our results show that the expectation values of the lowest nontrivial charges are nonzero for baryon and meson states but vanish for non-gauge-invariant states, supporting the interpretation that hadrons indeed carry these charges. While renormalization effects and higher-order contributions remain to be analyzed, these findings point toward a potential link between gauge-invariant charges and confinement.

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Phys. Rev. D 113, 034508– Published 24 February, 2026
  • Received 6 October 2025
  • Accepted 21 January 2026
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