Related papers: Symanzik effective actions in the large N limit

We define an effective action for spin foam models of quantum gravity by adapting the background field method from quantum field theory. We show that the Regge action is the leading term in the semi-classical expansion of the spin foam…

In this paper we study Zimmer's conjecture for $C^1$ actions of lattice subgroup of a higher-rank simple Lie group with finite center on compact manifolds. We show that when the rank of an uniform lattice is larger than the dimension of the…

We perform a lattice analysis of the Faddeev-Niemi effective action conjectured to describe the low-energy sector of SU(2) Yang-Mills theory. To this end we generate an ensemble of unit vector fields ("color spins") n from the Wilson…

We investigate conformal actions of cocompact lattices in higher-rank simple Lie groups on compact pseudo-Riemannian manifolds. Our main result gives a general bound on the real-rank of the lattice, which was already known for the action of…

Models of Dynamical Electroweak Symmetry Breaking are expected to display a quasi-conformal scaling behaviour in order to accommodate experimental constraints. The scaling properties of a theory can be studied using finite volume…

The action of the 2d O(3) non-linear sigma model on the lattice in a bath of particles, when expressed in terms of standard O(3) degrees of freedom, is complex. A reformulation of the model in terms of new variables that makes the action…

We derive three-dimensional, Z(N)-symmetric effective actions in terms of Polyakov loops by means of strong coupling expansions, starting from thermal SU(N) Yang-Mills theory in four dimensions on the lattice. An earlier action in the…

We study scaling properties and topological aspects of the 2--d O(3) non--linear $\sigma$--model on the lattice with the parametrized fixed point action recently proposed by P.~Hasenfratz and F.~Niedermayer. The behavior of the mass gap…

We report on the determination of the deconfining temperature in SU(3) pure gauge theory, using the Symanzik tree level improved action, on lattices of size 3 x 12^3, 4 x 16^3, 5 x 20^3, 6 x24^3. We find that the asymptotic scaling…

We study smooth actions by lattices in higher-rank simple Lie groups. Assuming one element of the action acts with positive topological entropy, we prove a number of new rigidity results. For lattices in $\mathrm{SL}(n,\mathbb{R})$ acting…

For the O(N) sigma-model we studied the improvement program for actions with two- and four-spin interactions. An interesting example is an action which is reflection-positive, on-shell improved, and has all the coupling defined on an…

We consider lattice field theories with topological actions, which are invariant against small deformations of the fields. Some of these actions have infinite barriers separating different topological sectors. Topological actions do not…

We classify real-analytic $\mathrm{SL}(n,\mathbb{R})$-actions on closed manifolds of dimension m for $3\leq n\leq m\leq2n-3$, which extends Fisher--Melnick's work for $\mathrm{SL}(n,\mathbb{R})$-actions on closed n-manifolds. Additionally,…

In this paper, we study two-loop contribution to the effective action of a two-dimensional sigma model. We derive a new formula, which can be applicable to a regularization of general type. As examples, we obtain known results for…

A loop or coupling expansion of a so-called n-particle irreducible (nPI) generating functional provides a well-defined approximation scheme in terms of self-consistently dressed propagators and n-point vertices. A self-consistently complete…

The topics covered by the lectures include Symanzik's effective continuum theory, O(a) improvement, chiral symmetry on the lattice and non-perturbative renormalization.

We introduce the Callan-Symanzik method in the description of anisotropic as well as isotropic Lifshitz critical behaviors. Renormalized perturbation theories are defined by normalization conditions with nonvanishing masses and at zero…

We compute the beta-function and the anomalous dimension of all the non-derivative operators of the theory up to three-loops for the most general nearest-neighbour O(N)-invariant action together with some contributions to the four-loop…

Fixed point actions for free and interacting staggered lattice fermions are constructed by iterating renormalization group transformations. At large N the fixed point action for the Gross-Neveu model is a perfect action in the sense of…

We describe a functional method to obtain the exact evolution equation of the effective action with a parameter of the bare theory. When this parameter happens to be the bare mass of the scalar field, we find a functional generalization of…