Resurgence and $1/N$ Expansion in Integrable Field Theories
| Title: | Resurgence and $1/N$ Expansion in Integrable Field Theories |
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| Authors: | Di Pietro, Lorenzo, Mariño, Marcos, Sberveglieri, Giacomo, Serone, Marco |
| Publication Year: | 2021 |
| Collection: | Mathematics High Energy Physics - Lattice High Energy Physics - Phenomenology High Energy Physics - Theory Mathematical Physics |
| Subject Terms: | High Energy Physics - Theory, High Energy Physics - Lattice, High Energy Physics - Phenomenology, Mathematical Physics |
| More Details: | In theories with renormalons the perturbative series is factorially divergent even after restricting to a given order in $1/N$, making the $1/N$ expansion a natural testing ground for the theory of resurgence. We study in detail the interplay between resurgent properties and the $1/N$ expansion in various integrable field theories with renormalons. We focus on the free energy in the presence of a chemical potential coupled to a conserved charge, which can be computed exactly with the thermodynamic Bethe ansatz (TBA). In some examples, like the first $1/N$ correction to the free energy in the non-linear sigma model, the terms in the $1/N$ expansion can be fully decoded in terms of a resurgent trans-series in the coupling constant. In the principal chiral field we find a new, explicit solution for the large $N$ free energy which can be written as the median resummation of a trans-series with infinitely many, analytically computable IR renormalon corrections. However, in other examples, like the Gross-Neveu model, each term in the $1/N$ expansion includes non-perturbative corrections which can not be predicted by a resurgent analysis of the corresponding perturbative series. We also study the properties of the series in $1/N$. In the Gross-Neveu model, where this is convergent, we analytically continue the series beyond its radius of convergence and show how the continuation matches with known dualities with sine-Gordon theories. Comment: 59 pages, 5 figures |
| Document Type: | Working Paper |
| DOI: | 10.1007/JHEP10(2021)166 |
| Access URL: | http://arxiv.org/abs/2108.02647 |
| Accession Number: | edsarx.2108.02647 |
| Database: | arXiv |
| DOI: | 10.1007/JHEP10(2021)166 |
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