Related papers: Resurgence and $1/N$ Expansion in Integrable Field…
In this thesis we explore the physics of renormalons in integrable models under the framework of resurgence. In the first part, we review some background on resurgence, integrability and renormalons, including a discussion of large N…
In integrable field theories in two dimensions, the Bethe ansatz can be used to compute exactly the ground state energy in the presence of an external field coupled to a conserved charge. We generalize previous results by Volin and we…
There has been recently considerable progress in understanding the nature of perturbation theory in UV free and gapped $2d$ integrable field theories with renormalon singularities. Thanks to Bethe ansatz and large $N$ techniques,…
We present new results on the Gross-Neveu model at finite temperature and at next-to-leading order in the 1/N expansion. In particular, a new expression is obtained for the effective potential which is explicitly invariant under…
The previously developed renormalizable perturbative 1/N-expansion in higher dimensional scalar field theories is extended to gauge theories with fermions. It is based on the $1/N_f$-expansion and results in a logarithmically divergent…
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 ground state energy of integrable asymptotically free theories can be conjecturally computed by using the Bethe ansatz, once the theory has been coupled to an external potential through a conserved charge. This leads to a precise…
Due to instanton effects, gauge-theoretic large N expansions yield asymptotic series, in powers of 1/N^2. The present work shows how to generically make such expansions meaningful via their completion into resurgent transseries, encoding…
We study the free energy of integrable, asymptotically free field theories in two dimensions coupled to a conserved charge. We develop methods to obtain analytic expressions for its trans-series expansion, directly from the Bethe ansatz…
We introduce a non-perturbative continuum framework to study the dynamics of quantum field theory (QFT), applied here to the CP(N-1) model, using Ecalle's theory of resurgent trans-series, combined with the physical principle of continuity,…
In the first part of this lecture, the 1/N expansion technique is illustrated for the case of the large-N sigma model. In large-N gauge theories, the 1/N expansion is tantamount to sorting the Feynman diagrams according to their degree of…
The exact mass gap of the O(N) Gross-Neveu model is known, for arbitrary $N$, from non-perturbative methods. However, a "naive" perturbative expansion of the pole mass exhibits an infinite set of infrared renormalons at order 1/N, formally…
We reconsider in some detail a construction allowing (Borel) convergence of an alternative perturbative expansion, for specific physical quantities of asymptotically free models. The usual perturbative expansions (with an explicit mass…
We demonstrate how one can construct renormalizable perturbative expansion in formally nonrenormalizable higher dimensional field theories. It is based on $1/N_f$-expansion and results in a logarithmically divergent perturbation theory in…
Perhaps the simplest IR renormalon occurs in the ground state energy of a superrenormalizable model, the scalar $O(N)$ theory in two dimensions with a quartic potential and negative squared mass. We show that this renormalon, found…
We demonstrate how one can construct renormalizable perturbative expansion in formally nonrenormalizable higher dimensional scalar theories. It is based on 1/N-expansion and results in a logarithmically divergent perturbation theory in…
Under certain assumptions and independent of the instantons, we show that the logarithm expansion of dimensional regularization in quantum field theory needs a nonperturbative completion to have a renormalization-group flow valid at all…
Many observables in quantum field theory can be expressed in terms of trans-series, in which one adds to the perturbative series a typically infinite sum of exponentially small corrections, due to instantons or to renormalons. Even after…
Apparently convergent contributions of resummed perturbative series at the next-to-leading order of the 1/N expansion in the O(N) model are reanalyzed in terms of renormalizability. Compared to our earlier article [G. Fejos et al., Phys.…
We study the $O(2N)$ symmetric Gross-Neveu model at finite density in the presence of a $U(1)$ chemical potential $h$ for a generic number $a \leq N-2$ of fermion fields. By combining perturbative quantum field theory, semiclassical large…