We present evidence for the universality of the continuum limit of the scale dependence of the renormalization constant associated with the operator corresponding to the average momentum of non-singlet parton densities. The evidence is provided by a non-perturbative computation in quenched lattice QCD using the Schrödinger Functional scheme. In particular, we show that the continuum limit is in...

ππ scattering length in the I = 2 channel is calculated within quenched approximation using improved gauge and improved Wilson fermion actions on anisotropic lattices. The results are extrapolated towards the chiral, infinite volume and continuum limit. This result improves our previous result on the scattering length. In the chiral, infinite volume and continuum limit, we obtain a (2) 0 mπ = −...

We discuss the Schrödinger functional in lattice QCD with staggered fermions including its order O(a) boundary counterterms. We relate it, in the classical continuum limit, to the Schrödinger functional as obtained in the same limit with Wilson fermions. We compute the strong coupling constant defined via the Schrödinger functional with staggered fermions at one loop and show that it agrees wit...

We study the continuum scaling limit of some statistical mechanical models deened by convex Hamiltonians which are gradient perturbations of a massless free eld. By proving a central limit theorem for these models, we show that their long distance behavior is identical to a new (homogenized) continuum massless free eld. We shall also obtain some new bounds on the 2-point correlation functions o...

In this lecture we provide two examples of problems where reasonable models are given by the deterministic continuum limit of the discrete random walk through which the problem is naturally defined. Once suitably defined, this continuum limit usually takes the form of a partial differential equation (hence deterministic). One interesting use of the continuum limit we will see in upcoming lectur...

We study discrete vortices in the anti-continuum limit of the discrete two-dimensional nonlinear Schrödinger (NLS) equations. The discrete vortices in the anti-continuum limit represent a finite set of excited nodes on a closed discrete contour with a non-zero topological charge. Using the Lyapunov–Schmidt reductions, we find sufficient conditions for continuation and termination of the discret...

We formulate a Euclidean spacetime lattice whose continuum limit is (2, 2) supersymmetric Yang-Mills theory in two dimensions, a theory which possesses four supercharges and an anomalous global chiral symmetry. The lattice action respects one exact supersymmetry, which allows the target theory to emerge in the continuum limit without fine-tuning. Our method exploits an orbifold construction des...

Any μ2-divergence is shown analytically to be absent for a class of actions for Overlap and Domain Wall Fermions with nonzero chemical potential. All such actions are, however, shown to violate the chiral invariance. While the parameter M of these actions can be shown to be irrelevant in the continuum limit, as expected, it is shown numerically that the continuum limit can be reached with relat...

The advantage of this action is that the Dirac operator remains non-singular when m = 0 so that we can work in the chiral limit. Note that we have an exact chiral symmetry generated by γ5ξ5 which means we will have a massless pion at m = 0 when this symmetry is spontaneously broken. The 4-fermion term is an irrelevant operator, so this theory should have the same continuum limit — continuum QCD...

We study the continuum scaling limit of some statistical mechanical models de ned by convex Hamiltonians which are gradient perturbations of a massless free eld. By proving a central limit theorem for these models, we will show that their long distance behavior is identical to a new (homogenized) continuum massless free eld. We shall also obtain some new bounds on the two point functions of the...