Twisted space-time reduced model of large N QCD with two adjoint Wilson fermions

TL;DR

This paper constructs and analyzes a twisted space-time reduced model of large N QCD with two adjoint Wilson fermions, demonstrating that choosing appropriate flux parameters yields results consistent with large volume lattice models, unlike the simpler periodic case.

Contribution

The paper introduces a twisted boundary condition approach for the large N QCD reduced model, showing improved stability and physical relevance over the zero-flux case.

Findings

Twisted boundary conditions preserve symmetry and improve N-dependence.

The model with non-zero flux matches large volume lattice results for Wilson loops.

Zero-flux model shows irregular N-dependence, making it less practical.

Abstract

The space-time reduced model of large N QCD with two adjoint Wilson fermions is constructed by applying the symmetric twist boundary conditions with non-vanishing flux $k$. For large but finite $N=L^2$, the model should behave as the large N version of the ordinary lattice gauge model on a $V=L^4$ space-time volume. We perform a comparison of the $N$ dependence of several quantities in this model and in the $k$=0 model (corresponding to periodic boundary conditions). Although the Z$^4$(N) symmetry seems unbroken in all cases, the N-dependence analysis favours the use of the same values of $k$ and $L$ for which the symmetry is also unbroken in the pure gauge case. In particular, the $k=0$ model, studied recently by several authors, shows a large and irregular dependence on $N$ within our region of parameters. This makes this reduced model very impractical for extracting physical information about the large N lattice theory. On the contrary, the model for $N=289=17^2$ and large enough $k$ gives consistent results, even for extended observables as Wilson loops $W(R,T)$ up to $R,T$=8, matching the expected behaviour for the lattice model with a $17^4$ space-time volume.