Appearance and disappearance of thermal renormalons

Abstract

We consider a scalar field model with a gφ 4 4 interaction and compute the mass correction at next-to-leading order in a large-N expansion to study the summability of the perturbative series. It is already known that at zero temperature this model has a singularity in the Borel plane (a "renormalon"). We find that a small increase in temperature adds two countable sets both with an infinite number of renormalons. For one of the sets the position of the poles is thermal independent and the residue is thermal dependent. In the other one both the position of poles and the residues are thermal dependent. If we consider the model at extremely high temperatures, however, one observes that all the renormalons disappear and the model becomes Borel summable.R 3 × S 1 [20] and the CP N −1 non-linear sigma model on arXiv:1804.10708v2 [hep-th]

A recursive enumeration of connected Feynman diagrams with an arbitrary number of external legs in the fermionic non-relativistic interacting gas

“…Although the enumeration of the Feynman diagrams is independent of the integrals that represent the physical processes, when we take the total contribution of certain classes of diagrams, the global structure of the generative combinatorics is relevant. (This can be seen, for instance, in recent results [7], where the symmetry factor -or multiplicity-of the related Feynman diagrams appear explicitly in the integrals. )…”

“…This is easy to see: In expression (7), there are 2m + N annihilation field operators (N different ψ(x i ), m different ψ(z j ) and m different ψ(z k )) and 2m + N creation field operators (N different ψ † (y i ), m different ψ † (z j ) and m different ψ † (z k ).) Non-vanishing contractions only happen between creation and annihilation operators.…”

“…Expression ( 21) is only one particular case of ( 12) and ( 13). If we add all other possible cases, we obtain N (N ) m , namely, the number of total contractions in (7),…”

Renormalons in a scalar self interacting theory: thermal, thermomagnetic and thermoelectric corrections for all values of temperature

“…For a classical review, see [5]. Recently there has been a renewed interest in the subject by considering one loop renormalization group equation in multi-field theories [6] or by considering finite temperature mass correction in the λφ 4 theory, reanalyzing the temperature dependence of poles and their residues [7]. Quite recently, the relation between renormalons and analytic trans-series has been considered in the context of field theories in two dimensions [8].…”

Thermomagnetic renormalons in a scalar self-interacting $λϕ^4$ theory

“…For a review, see [5]. Recently there has been a renewed interest in the subject by considering one loop renormalization group equation in multi-field theories [6] or by considering finite temperature mass correction in the λφ 4 theory, reanalyzing the temperature dependence of poles and their residues [7]. There are other sources of divergences, as instantons in quantum chromodynamics (QCD) [8,9], for example.…”