Color structure of Yang-Mills theory with static sources in a periodic box

L. Giusti, A. L. Guerrieri, S. Petrarca, A. Rubeo, and M. Testa
Phys. Rev. D 92, 034515 – Published 26 August 2015

Abstract

We present an exploratory numerical study on the lattice of the color structure of the wave functionals of the SU(3) Yang–Mills theory in the presence of a qq¯ static pair. In a spatial box with periodic boundary conditions, we discuss the fact that all states contributing to the Feynman propagation kernel are global color singlets. We confirm this numerically by computing the correlations of gauge-fixed Polyakov lines with color-twisted boundary conditions in the time direction. The values of the lowest energies in the color singlet and octet external source sectors agree within statistical errors, confirming that both channels contribute to the lowest (global singlet) state of the Feynman kernel. We then study the case of homogeneous boundary conditions in the time direction for which the gauge fixing is not needed. In this case, the lowest energies extracted in the singlet external source sector agree with those determined with periodic boundary conditions, while in the octet sector, the correlator is compatible with being null within our statistical errors. Therefore, consistently only the singlet external source contribution has a nonvanishing overlap with the null-field wave functional.

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  • Received 27 May 2015

DOI:https://doi.org/10.1103/PhysRevD.92.034515

© 2015 American Physical Society

Authors & Affiliations

L. Giusti1, A. L. Guerrieri2, S. Petrarca3, A. Rubeo4, and M. Testa3

  • 1Dipartimento di Fisica and INFN, Università di Milano-Bicocca, Piazza della Scienza 3, I-20126 Milano, Italy
  • 2Dipartimento di Fisica and INFN, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, I-00133 Roma, Italy
  • 3Dipartimento di Fisica and INFN, Università di Roma La Sapienza, P.le Aldo Moro 5, I-00185 Roma, Italy
  • 4School of Mathematics, Trinity College, Dublin 2, Ireland

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Issue

Vol. 92, Iss. 3 — 1 August 2015

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