Testing volume independence of SU(N) pure gauge theories at large N

Abstract

In this paper we present our results concerning the dependence of Wilson loop expectation values on the size of the lattice and the rank of the SU(N) gauge group. This allows to test the claims about volume independence in the large N limit, and the crucial dependence on boundary conditions. Our highly precise results provide strong support for the validity of the twisted reduction mechanism and the TEK model, provided the fluxes are chosen within the appropriate domain.

Perturbative contributions to Wilson loops in twisted lattice boxes and reduced models

“…[47], concluding that to avoid the problem one should scale appropriately the unique flux parameter k of the model when taking the large N limit. The validity of volume reduction under these premises has been verified in very precise measurements of Wilson loops [48]. Similar constraints are found when analyzing 2+1 dimensional theories defined on a spatial torus with twist [39,49].…”

A comparison of updating algorithms for large N reduced models

“…In particular, the one-site twisted Eguchi-Kawai model (TEK) [6] with fluxes chosen in a suitable range [7] has been tested recently in several works. There is now strong numerical evidence that its results for various lattice observables coincide with those of SU(N ) gauge theories extrapolated to N → ∞ [13]. Furthermore, the tests have also extended to physical quantities in the continuum limit such as the string tension [14] or the renormalized running coupling [15].…”

The twisted gradient flow coupling at one loop

“…From the point of view of perturbative calculations, TBC have an enormous advantage over periodic ones (PBC), as using TBC turns the set of zero-action solutions into a discrete one, and avoids the quartic nature of the fluctuations around A µ = 0 present with PBC [21]. The usefulness of TBC for perturbation theory was first formulated in the context of volume reduction in large N Yang-Mills theory [22,23], and was then extended to various other contexts at finite and large N [24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. Despite these advantanges, as we will show along this work, perturbative calculations in the twisted gradient flow scheme remain challenging, although so far an analogous perturbative calculation in the case of periodic boundary conditions has not been obtained.…”

“…Proof for this statement relies on the independence of the large N Schwinger-Dyson equations from lattice volume, which in turn requires center symmetry to be preserved. As the symmetry was shown not to hold with PBC [46], several alternative proposals were formulated [42,[46][47][48][49], one of which was the use of twisted boundary conditions [22,23], which has proven very successful provided the twist tensor is judiciously chosen [35,36,[50][51][52][53][54][55]. The idea of volume reduction with TBC was extended to the continuum theory in ref.…”