Bifurcations with nonuniversal exponents in a lattice model

The bifurcations of a two-dimensional area preserving mapping with a cubic term are studied. This mapping shows a large number of bifurcations where the period becomes a multiple. For a given order of bifurcation exponents are found which depend on the series considered. The exponents calculated numerically are compared with renormalisation calculations for a number of cases.     

Renormalisation group and two-point functions in bosonic σ models

The renormalisation group equations for two-point functions involving the energy-momentum tensor in two-dimensional non-linear σ models derived previously using dimensional regularisation are solved to give the leading singular term in the operator product expansion. The results are in accord with the general framework suggested by Zamolodchikov, although the equation describing the renormalisation flow of the Virasoro central charge takes a modified form.     

Instanton calculus and the β function in supersymmetric yang-mills theories

We study recent arguments that the higher order quantum corrections to the vacuum energy in the presence of an instanton background field in supersymmetric Yang-Mills theories are zero. We conclude that these arguments are invalid. This is in spite of the fact that, with the use of the renormalisation group, they lead to the correct results for the coefficients in the β-function which are independent of the renormalisation scheme.     

Gradient properties of the renormalisation group equations in multicomponent systems

The existence of a metric, which enables the renormalisation group β functions of a multicomponent field theory to be written as a gradient, has very important implications for the asymptotic behavior of the renormalisation group equations. It is shown that a very simple metric exists in a field theory with n-component Bose fields and arbitrary φ⁴ interaction, when the β functions are calculated perturbatively up to and including the 2-loop diagrams. This same metric is shown to work for all irreducible diagrams, but it must and can be modified to accommodate reducible 3-loop contributions. The prospects and outlook of this aspect of the renormalisation group are discussed.     

A contribution to the problem of effective particle-hole interactions

Various effects arising in nuclear-structure calculations and leading all to a renormalisation of the nucleon-nucleon interaction are reviewed. A new treatment is proposed for the renormalisation due to mixing of the particle-hole subspace and then particle ?n hole (n=2, 3, 4 etc.) subspaces.     

Dilaton dependence of the two-loop effective action

We construct a family of equivalent two-loop string theory effective actions, incorporating dilaton background field contributions, which subsumes all those presently available in the literature. We identify in particular two one-parameter subsets of this family, one of which consists of actions with no dilaton dependence (beyond an overall factor) and another which corresponds in a natural way to renormalisation scheme dependence in the underlying non-linear σ-model. Corresponding to the family of actions we construct a family of renormalisation group dilaton β-functions and show that they are related by renormalisation group transformations.     

Dynamical Casimir Effect for Scalar Fields II (Energy Calculation)

The energy of the evolved vacuum state is calculated. From a frequency cut-off regularisation the divergent terms are separated and, in the 1 + 1 dimensional case they are removed with a mass renormalisation of the moving boundary. A renormalisation of the external force is also needed in 3 + 1 dimensions. PACS Subject Classifications: 42.50.Lc, 03.70.+k, 11.10.Ef.     

One-loop renormalisation of superfield Yang-Mills theories

We calculate the one-loop ultraviolet and infrared divergences in superfield Yang-Mills theories to fourth order in the gauge field. The ultraviolet divergences require a non-linear field renormalisation, and graphs with external ghost fields show that a non-linear renormalisation of the gauge-fixing function is also needed. These observations are confirmed by calculations incorporating matter fields, which are used to extend the result to all orders for the special case of SU(2). On the other hand the infrared divergences, which occur in general gauges, are apparently impossible to remove in any acceptable way.     

The σ-model and its renormalization in a dimensionally regularised normal product formulation

The σ-model is re-examined in the light of the reformulation of the normal product method in dimensional regularisation. It is considered both as a prime example of, and testing ground for, these methods, and to display the dimensionally regularised renormalisation of the model. Explicit and spontaneous symmetry breakings are considered, and the PCAC relation and Goldstone theorem are examined and proved in the one loop approximation. The renormalisation group equation coefficients are also obtained to this order. Both arbitrary (renormalised) parametrisations, and the mass shell parametrisation with finite counterterms are considered. It is found that, in contrast with other treatments, these counter terms remain finite in the infra-red limit of a massless symmetric Lagrangian.     

From entanglement renormalisation to the disentanglement of quantum double models

We describe how the entanglement renormalisation approach to topological lattice systems leads to a general procedure for treating the whole spectrum of these models in which the Hamiltonian is gradually simplified along a parallel simplification of the connectivity of the lattice. We consider the case of Kitaev’s quantum double models, both Abelian and non-Abelian, and we obtain a rederivation of the known map of the toric code to two Ising chains; we pay particular attention to the non-Abelian models and discuss their space of states on the torus. Ultimately, the construction is universal for such models and its essential feature, the lattice simplification, may point towards a renormalisation of the metric in continuum theories.     

Analytic study of the self-similarity of the density of states for one-dimensional quasicrystals

In this Letter the self-similarity of the density of states (DOS) for the Fibonacci chain is studied analytically by the Green function and renormalisation group approach.     

Renormalisation group flow and geodesics in the O(N) model for large N

A metric is introduced on the space of parameters (couplings) describing the large N limit of the O(N) model in Euclidean space. The geometry associated with this metric is analysed in the particular case of the infinite volume limit in three dimensions and it is shown that the Ricci curvature diverges at the ultra-violet (Gaussian) fixed point but is finite and tends to constant negative curvature at the infra-red (Wilson-Fisher) fixed point. The renormalisation group flow is examined in terms of geodesics of the metric. The critical line of cross-over from the Wilson-Fisher fixed point to the Gaussian fixed point is shown to be a geodesic but all other renormalisation group trajectories, which are repulsed from the Gaussian fixed point in the ultraviolet, are not geodesics. The geodesic flow is interpreted in terms of a maximisation principle for the relative entropy.     

Computation of Dimensions for Strange Attractors by the Box Counting Renormalization Method

The scaling ansats for box counting functions is verified numerically for the reverse doubling sequence of the logistic map. A box counting renormalisation method is developed to calculate dimensions for strange attractors.     

On the reality of the eigenvalues of the linearized renormalisation group transformations on a lattice

We show that the eigenvalues of the T-matrix of the renormalisation group equations on a lattice linearized around a fixed point, are always real although the matrix is non-symmetric.     

Extra dimension searches at hadron colliders to next-to-leading order-QCD

The quantitative impact of NLO-QCD corrections for searches of large and warped extra dimensions at hadron colliders are investigated for the Drell-Yan process. The K-factor for various observables at hadron colliders are presented. Factorisation, renormalisation scale dependence and uncertainties due to various parton distribution functions are studied. Uncertainties arising from the error on experimental data are estimated using the MRST parton distribution functions.      

On the renormalisation group for the boundary truncated conformal space approach

In this paper we continue the study of the truncated conformal space approach to perturbed boundary conformal field theories. This approach to perturbation theory suffers from a renormalisation of the coupling constant and a multiplicative renormalisation of the Hamiltonian. We show how these two effects can be predicted by both physical and mathematical arguments and prove that they are correct to leading order for all states in the TCSA system. We check these results using the TCSA applied to the tri-critical Ising model and the Yang–Lee model. We also study the TCSA of an irrelevant (non-renormalisable) perturbation and find that, while the convergence of the coupling constant and energy scales are problematic, the renormalised and rescaled spectrum remain a very good fit to the exact result, and we find a numerical relationship between the IR and UV couplings describing a particular flow. Finally we study the large coupling behaviour of TCSA and show that it accurately encompasses several different fixed points.     

Asymptotic near freedom

The possibility that the asymptotic behaviour of the structure functions for electroproduction or neutrinoproduction is controlled by a renormalisation group fixed point near the origin, but not at the origin, is discussed.