Simulations of a partially reduced twisted Eguchi-Kawai model with one adjoint Dirac fermion show the Polyakov loop remains near zero for periodic boundary conditions as the compactified circle shrinks, supporting adiabatic continuity of the confined phase.
Tachyonic instabilities in 2 + 1 dimensional Yang–Mills theory and its connection to number theory
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abstract
We consider the $2+1$ dimensional Yang-Mills theory with gauge group $\text{SU}(N)$ on a flat 2-torus under twisted boundary conditions. We study the possibility of phase transitions (tachyonic instabilities) when $N$ and the volume vary and certain chromomagnetic flux associated to the topology of the bundle can be adjusted. Under natural assumptions about how to match the perturbative regime and the expected confinement, we prove that the absence of tachyonic instabilities is related to some problems in number theory, namely the Diophantine approximation of irreducible fractions by other fractions of smaller denominator.
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Gradient-flow scales are set for SU(3), SU(5), SU(8) and large-N Yang-Mills down to 0.025 fm using twisted volume reduction and topology-taming algorithms.
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Adiabatic continuity in a partially reduced twisted Eguchi-Kawai model with one adjoint Dirac fermion
Simulations of a partially reduced twisted Eguchi-Kawai model with one adjoint Dirac fermion show the Polyakov loop remains near zero for periodic boundary conditions as the compactified circle shrinks, supporting adiabatic continuity of the confined phase.
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Scale setting of SU($N$) Yang--Mills theory, topology and large-$N$ volume independence
Gradient-flow scales are set for SU(3), SU(5), SU(8) and large-N Yang-Mills down to 0.025 fm using twisted volume reduction and topology-taming algorithms.