PoS - Proceedings of Science
Volume 396 - The 38th International Symposium on Lattice Field Theory (LATTICE2021) - Oral presentation
Coarse graining in effective theories of lattice QCD in 1+1d and 2+1d
C. Konrad* and O. Philipsen
Full text: pdf
Pre-published on: May 16, 2022
Published on: July 08, 2022
In the strong coupling and heavy quark mass regime, lattice QCD dimensionally reduces to effective theories of
Polyakov loops depending on the parameters of the original Wilson action $\beta, \kappa$ and $N_\tau$. We apply coarse graining techniques to such theories in 1d and 2d, corresponding to lattice QCD at finite temperature
and non-zero chemical potential in 1+1d and 2+1d, respectively. In 1d the method is applied to the effective theories up to $\mathcal{O}(\kappa^4)$. Using the transfer matrix, the recursion relations are solved analytically. The thermodynamic limit is taken for some observables. Afterwards, continuum extrapolation is performed numerically and results are discussed. In 2d the coarse graining method is applied in the pure gauge and static quark limit. Running couplings are obtained and the fixed points of the transformations are discussed. Finally, the critical coupling of the deconfinement transition is determined in both limits. Agreement to about 12% with Monte Carlo results of 2+1d Yang-Mills theory from the literature is observed.
DOI: https://doi.org/10.22323/1.396.0159
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