Asymptotics in an Asymptotic CFT

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In this work we illustrate the resurgent structure of the λ-deformation; a two-dimensional integrable quantum field theory that has an RG flow with an SU(N) k Wess-Zumino-Witten conformal fixed point in the UV. To do so we use modern matched asymptotic techniques applied to the thermodynamic Bethe ansatz formulation to compute the free energy to 38 perturbative orders in an expansion of large applied chemical potential. We find numerical evidence for factorial asymptotic behaviour with both alternating and non-alternating character which we match to an analytic expression. A curiosity of the system is that the leading non-alternating factorial growth vanishing when k divides N. The ambiguities associated to Borel resummation of this series are suggestive of non-perturbative contributions. This is verified with an analytic study of the TBA system demonstrating a cancellation between perturbative and non-perturbative ambiguities.

Original languageEnglish
Publisherspringer link
Number of pages29
Publication statusPublished - 24 Apr 2023

Publication series

NameJournal of High Energy Physics
PublisherSpringer Verlag
ISSN (Print)1126-6708

Bibliographical note

Funding Information:
DCT is supported by The Royal Society through a University Research FellowshipGeneralised Dualities in String Theory and Holography URF 150185 and in part by STFC grant ST/P00055X/1 as well as by the FWO-Vlaanderen through the project G006119N and Vrije Universiteit Brussel through the Strategic Research Program “High-Energy Physics”. LS is supported by a PhD studentship from The Royal Society and the grant RF\ERE\210269. For the purpose of open access, the authors have applied a Creative Commons Attribution (CC BY) licence to any Author Accepted Manuscript version arising. We thank M Mariño and T Reis for helpful comments on a draft and I Aniceto for comments relating to this project.

Publisher Copyright:
© 2023, The Author(s).


  • hep-th
  • math-ph
  • math.MP
  • nlin.SI


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