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Quantum Yang-Mills Charges in Strongly Coupled 2D Lattice QCD with Three Flavors

Paulo A. Faria da Veiga, Luiz A. Ferreira, Henrique Malavazzi, Ravi Mistry

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 non-trivial 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.

Quantum Yang-Mills Charges in Strongly Coupled 2D Lattice QCD with Three Flavors

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 non-trivial 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.

Paper Structure

This paper contains 15 sections, 112 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Framework and Preliminaries
  3. The classical charge operator and conserved charges
  4. 1+1 quantum lattice Wilson action: pure gauge and matter
  5. Path integral: expectation values on the lattice
  6. Quantum Yang-Mills charges on the lattice
  7. Lattice charge operator
  8. State vector analysis: expectation values for mesons and baryons
  9. Matter part
  10. Gauge part
  11. Total contribution: summing expectation values
  12. Conclusion
  13. Non-zero contributions
  14. Computational results
  15. The naive continuum limit: covariantly conserved matter current

Figures (2)

  • Figure 1: The plaquette: a depiction of bonds connecting the nearest neighbour points.
  • Figure 2: A tree diagram for the fermionic part of the expectation values taken with respect to meson composite vector fields with $y=x$, $\rho=0$ and $\pi=+1$.

Theorems & Definitions (5)

  • Remark 2.1
  • Remark 3.1
  • Remark 3.2
  • Remark 3.3
  • Remark B.1