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To set the stage, I discuss the $beta$-function of the massless O(N) model in three dimensions, which can be calculated exactly in the large N limit. Then, I consider SU(N) Yang-Mills theory in 2+1 space-time dimensions. Relating the $beta$-function to the expectation value of the action in lattice gauge theory, and the latter to the trace of the energy-momentum tensor, I show that $frac{d ln g^2/mu}{dln mu}=-1$ for all $g$ and all N in one particular renormalization scheme. As a consequence, I find that the Yang-Mills $beta$-function in three dimensions must have the same sign for all finite and positive bare coupling parameters in any renormalization scheme, and all non-trivial infrared fixed points are unreachable in practice.
By using the method of center projection the center vortex part of the gauge field is isolated and its propagator is evaluated in the center Landau gauge, which minimizes the open 3-dimensional Dirac volumes of non-trivial center links bounded by the
We solve exactly the Dyson-Schwinger equations for Yang-Mills theory in 3 and 4 dimensions. This permits us to obtain the exact correlation functions till order 2. In this way, the spectrum of the theory is straightforwardly obtained and comparison w
The width of the quantum delocalization of the QCD strings is investigated in effective string models beyond free Nambu-Goto approximation. We consider two Lorentzian-invariant boundary-terms in the Luscher-Weisz string action in addition to self-int
We review our recent work on the glueball spectrum of pure Yang-Mills theory in 2+1 dimensions. The calculations make use of Karabali-Nair corner variables in the Hamiltonian formalism, and involve a determination of the leading form of the ground-state wavefunctional.
We study the infrared behavior of the effective Coulomb potential in lattice SU(3) Yang-Mills theory in the Coulomb gauge. We use lattices up to a size of 48^4 and three values of the inverse coupling, beta=5.8, 6.0 and 6.2. While finite-volume effec