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Trans-series from condensates
by Marcos Mariño, Ramon Miravitllas
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Submission summary
| Authors (as registered SciPost users): | Marcos Mariño · Ramon Miravitllas |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202501_00059v1 (pdf) |
| Date accepted: | 2025-02-26 |
| Date submitted: | 2025-01-31 12:28 |
| Submitted by: | Miravitllas, Ramon |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
The Shifman-Vainshtein-Zakharov (SVZ) sum rules provide a method to obtain trans-series expansions in many quantum field theories, in which exponentially small corrections are calculated by combining the operator product expansion with the assumption of vacuum condensates. In some solvable models, exact expressions for trans-series can be obtained from non-perturbative results, and this makes it possible to test the SVZ method by comparing its predictions to these exact trans-series. In this paper we perform such a precision test in the example of the fermion self-energy in the Gross-Neveu model. Its exact trans-series expansion can be extracted from the large $N$ solution, at the first non-trivial order in $1/N$. It is given by an infinite series of exponentially small corrections involving factorially divergent power series in the 't Hooft parameter. We show that the first two corrections are associated to two-quark and four-quark condensates, and we reproduce the corresponding power series exactly, and at all loops, by using the SVZ method. In addition, the numerical values of the condensates can be extracted from the exact result, up to order $1/N$.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
List of changes
1) We added a footnote with a reference to the paper by Anselm (ref. 24) and to a paper by M. Shifman with a historical appraisal of Anselm’s work.
2) We have corrected the phrasing of the third paragraph in p. 2.
3) We have added two additional references on recent studies of renormalons in two-dimensional models (refs. 8 and 9).
4) We have corrected a misprint in a previous version of eq. (4.22).
5) We have made a short clarification concerning the OPE in position vs momentum space in p. 19, and refer to a paper by Novikov et al. (ref. 44) for a discussion on this point.
6) We have now collected and slightly enlarged the discussion on the change of scheme at the end of section 3.1. We have also pointed out that the result on the anomalous dimension of the field in 3.15 follows from the finiteness of the 1/N correction to the momentum part of the self-energy.
7) We have added a comment in the third paragraph of the conclusions (p. 36) stating that there are no additional sources of exponentially small corrections in our calculation, in particular no instanton corrections. We also added a comment on the probable absence of large N instanton corrections and referred to an old paper of Avan and de Vega on this point.
Published as SciPost Phys. 18, 101 (2025)
Reports on this Submission
Report #1 by Yizhuang Liu (Referee 2) on 2025-2-9 (Invited Report)
Report
The second version and the author's replies have addressed my concerns. I recommend publication.
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)