Related papers: The Massive O(N) Non-linear Sigma Model at High Or…
The off-shell dynamics of the O(3) nonlinear sigma-model is probed in terms of spectral densities and two-point functions by means of the form factor approach. The exact form factors of the Spin field, Noether-current, EM-tensor and the…
Within the non-perturbative 1/N expansion, we discuss numerical methods for calculating multi-loop Feynman graph needed to derive physical scattering amplitudes. We apply higher order 1/N methods to the scalar sector of the standard model,…
Recently it was shown that the scaling dimension of the operator $\phi^n$ in $\lambda(\phi^*\phi)^2$ theory may be computed semi-classically at the Wilson-Fisher fixed point in $d=4-\epsilon$, for generic values of $\lambda n$ and this was…
We consider the O(n) loop model on tetravalent maps and show how to rephrase it into a model of bipartite maps without loops. This follows from a combinatorial decomposition that consists in cutting the O(n) model configurations along their…
The O(n) non-linear $\sigma$-model is simulated on 2-dimensional regular and random lattices. We use two different levels of randomness in the construction of the random lattices and give a detailed explanation of the geometry of such…
We consider an $O(N)$ scalar field model with quartic interaction in $d$-dimensional Euclidean de Sitter space. In order to avoid the problems of the standard perturbative calculations for light and massless fields, we generalize to the…
We consider systems characterized by the presence of a rapidly oscillating force. A general method is presented for the construction of the effective action governing the large-scale nonlinear dynamics of such systems order by order in…
We calculate the finite volume mass gap $M(L)$ at 3-loop level in the non-linear O($n$) $\sigma$-model in two dimensions in small volumes. By applying the Monte Carlo measurements of the running coupling $\bar g^2(L)=2nM(L)L/(n-1)$ by…
A new class of truncation schemes of delta expansion on the lattice is studied. We show that the order of expansion in delta which is introduced as the dilation parameter can be taken large enough and the result gives rise to the Borel…
The non-diagonal correlators of vector and scalar currents are considered at three-loop order in QCD. The full mass dependence is computed in the case where one of the quarks is massless and the other one carries mass $M$. We exploit the…
The stochastic vacuum model description of a heavy meson is discussed in the context of a gauge invariant approach where Wilson loop expectation values appear naturally in the O($v^2$) spin-orbit Hamiltonian. These expectation values have…
We present a functional Schr\"{o}dinger picture formalism of the (1+1)-dimensional $O(N) $ nonlinear sigma model. The energy density has been calculated to two-loop order using the wave functional of a gaussian form, and from which the…
The O(N) non-linear sigma model in a $D$-dimensional space of the form ${\bf R}^{D-M} \times {\bf T}^M$, ${\bf R}^{D-M} \times {\bf S}^M$, or ${\bf T}^M \times {\bf S}^P$ is studied, where ${\bf R}^M$, ${\bf T}^M$ and ${\bf S}^M$ correspond…
We study a completely-packed loop model with crossings in a three-dimensional lattice and confirm it is described by $\mathrm{RP}^{n-1}$ sigma field theories. We use Monte Carlo simulations, with systems sizes up to…
We extend our investigation on a possible de Sitter symmetry breaking mechanism in non-linear sigma models. The scale invariance of the quantum fluctuations could make the cosmological constant time dependent signaling the de Sitter…
We report the results of a very high statistics Monte Carlo study of the continuum limit of the two dimensional O(3) non-linear $\sigma$ model. We find a significant discrepancy between the continuum extrapolation of our data and the form…
We report progress in the computation and analysis of strong-coupling series of two- and three-dimensional ${\rm O}(N)$ $\sigma$ models. We show that, through a combination of long strong-coupling series and judicious choice of observables,…
We continue the study, initiated in arXiv:1404.1094, of the $O(N)$ symmetric theory of $N+1$ massless scalar fields in $6-\epsilon$ dimensions. This theory has cubic interaction terms $\frac{1}{2}g_1 \sigma (\phi^i)^2 + \frac{1}{6}g_2…
A systematic study of large N expansion in supersymmetric theories are given. Supersymmetric O(N) non-linear sigma model in two and three dimensions, massless and massive supersymmetric QCD with $N_{f}<N_{c}-1$ and supergravity models are…
The $O(N)$ non-linear sigma model (NLSM) is an example of field theory on a target space with nontrivial geometry. One interesting feature of NLSM is asymptotic freedom, which makes perturbative calculations interesting. Given the successes…