New and old about renormalons: In memoriam Kolya Uraltsev

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 extract analytic results for the perturbative expansion of this observable, up to very high order, in various asymptotically free theories: the non-linear sigma model and its supersymmetric extension, the Gross-Neveu model, and the principal chiral field. We study the large order behavior of these perturbative series and we give strong evidence that, as expected, it is controlled by renormalons. Our analysis is sensitive to the next-to-leading correction to the asymptotics, which involves the first two coefficients of the beta function. We also show that, in the supersymmetric non-linear sigma model, there is no contribution from the first IR renormalon, in agreement with general arguments.

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“…In this sense, as pointed out in[18], the OPE gives a physical construction of the trans-series (3.1).…”

mentioning

confidence: 76%

Renormalons in integrable field theories

Mariño

Reis

2020

J. High Energ. Phys.

114

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“…The operator product expansion (OPE) connects perturbative information with non-perturbative condensates. The rate of the factorial divergences associated with infrared (IR) renormalons are identified with certain condensates of specific dimensions [57][58][59][60][61]. On R 2 , the exact large-N solution provides a rigorous realization of this idea.…”

Section: Semi-classical Realization Of Ir-renormalons As Neutral Bionsmentioning

confidence: 99%

Resurgence and dynamics of O(N) and Grassmannian sigma models

Dunne

Ünsal

2015

J. High Energ. Phys.

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We study the non-perturbative dynamics of the two dimensional O(N ) and Grassmannian sigma models by using compactification with twisted boundary conditions on R×S 1 , semi-classical techniques and resurgence. While the O(N ) model has no instantons for N > 3, it has (non-instanton) saddles on R 2 , which we call 2d-saddles. On R × S 1 , the resurgent relation between perturbation theory and non-perturbative physics is encoded in new saddles, which are associated with the affine root system of the o(N ) algebra. These events may be viewed as fractionalizations of the 2d-saddles. The first beta function coefficient, given by the dual Coxeter number, can then be intepreted as the sum of the multiplicities (dual Kac labels) of these fractionalized objects. Surprisingly, the new saddles in O(N ) models in compactified space are in one-to-one correspondence with monopole-instanton saddles in SO(N ) gauge theory on R 3 × S 1 . The Grassmannian sigma models Gr(N, M ) have 2d instantons, which fractionalize into N kink-instantons. The small circle dynamics of both sigma models can be described as a dilute gas of the one-events and two-events, bions. One-events are the leading source of a variety of non-perturbative effects, and produce the strong scale of the 2d theory in the compactified theory. We show that in both types of sigma models the neutral bion emulates the role of IR-renormalons. We also study the topological theta angle dependence in both the O(3) model and Gr(N, M ), and describe the multi-branched structure of the observables in terms of the theta-angle dependence of the saddle amplitudes.

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“…As pointed out in Shifman's review article [12], the study of renormalons is also important from a phenomenological perspective, as one needs, for instance, to know the solution at the nonperturbative level to obtain an estimate of the heavy-quark mass [19].…”

Section: Introductionmentioning

confidence: 99%

Appearance and disappearance of thermal renormalons

Cavalcanti¹,

Lourenço²,

Linhares³

et al. 2018

Phys. Rev. D

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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]

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New and old about renormalons: In memoriam Kolya Uraltsev

Cited by 28 publications

References 60 publications

Renormalons in integrable field theories

Renormalons in integrable field theories

Resurgence and dynamics of O(N) and Grassmannian sigma models

Appearance and disappearance of thermal renormalons

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