The deconfinement transition in SU(Nc) Yang–Mills is investigated by Monte Carlo simulations of the gauge theory discretized on a spacetime lattice. We present new results for 4⩽Nc⩽8 (in particular, ...for Nc=5 and Nc=7), which are analysed together with previously published results. The increased amount of data, the improved statistics and simulations closer to the continuum limit provide us with better control over systematic errors. After performing the thermodynamic limit, numerical results for the ratio of the critical temperature Tc over the square root of the string tension σ obtained on lattices with temporal extensions Nt=5,6,7,8 are extrapolated to the continuum limit. The continuum results at fixed Nc are then extrapolated to Nc=∞. We find that our data are accurately described by the formula Tc/σ=0.5949(17)+0.458(18)/Nc2. Possible systematic errors affecting our calculations are also discussed.
We conjecture that in Yang–Mills theories the ratio between the ground-state glueball mass squared and the string tension is proportional to the ratio of the eigenvalues of quadratic Casimir ...operators in the adjoint and the fundamental representations. The proportionality constant depends on the dimension of the space-time only, and is henceforth universal. We argue that this universality, which is supported by available lattice results, is a direct consequence of area-law confinement. In order to explain this universal behavior, we provide three analytical arguments, based respectively on a Bethe–Salpeter analysis, on the saturation of the scale anomaly by the lightest scalar glueball and on QCD sum rules, commenting on the underlying assumptions that they entail and on their physical implications.
We present a reformulation of the background field method for Yang-Mills type theories, based on using a superalgebra of generators of BRST and background field transformations. The new approach ...enables one to implement and consistently use non-linear gauges in a natural way, by using the requirement of invariance of the fermion gauge-fixing functional under the background field transformations.
It is shown that the gauge invariance and gauge dependence properties of effective action for Yang-Mills theories should be considered as two independent issues in the background field formalism. ...Application of this formalism to formulate the functional renormalization group approach is discussed. It is proven that there is a possibility to construct the corresponding average effective action invariant under the gauge transformations of background vector field. Nevertheless, being gauge invariant this action remains gauge dependent on-shell.
This article gives an explicit formula for the leading term of the free energy of three-dimensional U(N) lattice gauge theory for any N, as the lattice spacing tends to zero. The proof is based on a ...novel technique that avoids phase cell renormalization. The technique also yields a similar formula for the four-dimensional theory, but only in the weak coupling limit.
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