Related papers: Resurgence in the O(4) sigma model
We derive a systematic perturbative expansion for the finite-volume energy spectrum of the non-linear $O(N)$ $\sigma$-model in the $\delta$-regime. The violation of the power-counting rules that emerges after the separation of the fast and…
The possibility of the application of the free field representation developed by Lukyanov for massive integrable models is investigated in the context of the O(3) sigma model. We use the bootstrap fusion procedure to construct a free field…
Within the 1/N expansion of O(N) nonlinear $\sigma$ models for $d \leq 4$ it is possible to separate consistently the spin-wave and the massive-mode contributions to the scaling part of the free energy near criticality, and to evaluate them…
One-loop quantum corrections to the classical vortices in 2+1 dimensional O(3)-models are evaluated. Skyrme and Zeeman potential terms are used to stabilize the size of topological solitons. Contributions from zero modes, bound-states and…
We review \'Ecalle's formalism of minors, natural-majors and real-majors, and provide explicit formulas in the Borel plane that show the resurgence of the exponential of the Stirling series. We also discuss its Stokes phenomena in the…
We analyse the eigenvalue structure of the replicated transfer matrix of one-dimensional disordered Ising models. In the limit of $n \rightarrow 0$ replicas, an infinite sequence of transfer matrices is found, each corresponding to a…
We consider winding number transitions in the two dimensional O(3) non-linear sigma model, modified by a suitable conformal symmetry breaking term. We discuss the general properties of the relevant instanton solutions which dominate the…
By using the results of a high-statistics (O(10^7) measurements) Monte Carlo simulation we test several predictions of perturbation theory on the O(n) non-linear sigma-model in 2 dimensions. We study the O(3) and O(8) models on large enough…
This work is a step towards a non-perturbative continuum definition of quantum field theory (QFT), beginning with asymptotically free two dimensional non-linear sigma-models, using recent ideas from mathematics and QFT. The ideas from…
The paper contains successive description of the strong-coupling perturbation theory. Formal realization of the idea is based on observation that the path-integrals measure for absorption part of amplitudes $\R$ is Diracian ($\d$-like). New…
Four different types of free energies are computed by both thermodynamical Bethe Ansatz (TBA) techniques and by weak coupling perturbation theory in an integrable one-parameter deformation of the O(4) principal chiral sigma-model (with…
We compute the static self-energy of SU(3) gauge theory in four spacetime dimensions to order \alpha^{20} in the strong coupling constant. We employ lattice regularization to enable a numerical simulation within the framework of stochastic…
We study the effect of hedgehog suppression in the O(3) sigma model in D=2+1. We show via Monte Carlo simulations that the sigma model can be disordered while effectively forbidding these point topological defects. The resulting…
We study a quartic matrix model with partition function $Z=\int d\ M\exp{\rm Tr}\ (-\Delta M^2-\frac{\lambda}{4}M^4)$. The integral is over the space of Hermitian $(\Lambda+1)\times(\Lambda+1)$ matrices, the matrix $\Delta$, which is not a…
We study the O(2N) model at criticality in three dimensions in the double scaling limit of large N and large charge. We show that the large-charge expansion is an asymptotic series, and we use resurgence techniques to study the…
Based on the strong coupling expansion, we reinvestigate the scaling behavior of the susceptibility chi of two-dimensional O(N) sigma model on the square lattice by the use of Pade-Borel approximants. To exploit the Borel transform, we…
We calculate up to four loops the free energy of the two-dimensional (2D) O(n) nonlinear sigma-model regularized on the lattice with the 0-loop and 1-loop Symanzik improved actions. An effective coupling constant based on this calculation…
Vortices the $SO(2)$ gauged planar Skyrme model, with a) only Maxwell, b) only Chern-Simons, and c) both Maxwell and Chern-Simons dynamics are studied systematically. In cases a) and b), where both models feature a single parameter…
In Refs. [1,2] we determined the infinite volume coefficients of the perturbative expansions of the self-energies of static sources in the fundamental and adjoint representations in SU(3) gluodynamics to order $\alpha^{20}$. We used…
We study the simplest $SO(2)$ gauged $O(5)$ Skyrme models in $4+1$ (flat) dimensions. In the gauge decoupled limit, the model supports topologically stable solitons (Skyrmions) and after gauging, the static energy of the solutions is…