Research PapersNo Access

Non-Wilsonian ultraviolet completion via transseries

Alessio Maiezza

Ruder Bošković Institute, Bijenička cesta 54, 10000 Zagreb, Croatia

E-mail Address: amaiezza@irb.hr

Search for more papers by this author

and

Juan Carlos Vasquez

Amherst Center for Fundamental Interactions, Department of Physics, University of Massachusetts, Amherst, MA 01003, USA

E-mail Address: jvasquezcarm@umass.edu

Corresponding author.

Search for more papers by this author

https://doi.org/10.1142/S0217751X21500160Cited by:7 (Source: Crossref)

Abstract

We study some of the implications for the perturbative renormalization program when augmented with the Borel–Ecalle resummation. We show the emergence of a new kind of nonperturbative fixed point for the scalar $ϕ^{4}$ $ϕ^{4}$ model, representing an ultraviolet self-completion by transseries. We argue that this completion is purely non-Wilsonian and it depends on one arbitrary constant stemming from the transseries solution of the renormalization group equation. On the other hand, if no fixed points are demanded through the adjustment of this arbitrary constant, we end up with an effective theory in which the scalar mass is quadratically-sensitive to the cutoff, even working in dimensional regularization. Complete decoupling of the scalar mass to this energy scale can be used to determine a physical prescription for the Borel–Laplace resummation of the renormalons in nonasymptotically free models. We also comment on possible orthogonal scenarios available in the literature that might play a role when no fixed points exist.

Keywords:

PACS: 11.10.Gh

You currently do not have access to the full text article.
Recommend the journal to your library today!

References

1. G. ’t Hooft, Subnucl. Ser. 15, 943 (1979). Google Scholar
2. S. Weinberg, Ultraviolet Divergences in Quantum Theories of Gravitation (Harvard University, 1980), pp. 790–831. Google Scholar
3. K. Wilson and J. B. Kogut, Phys. Rep. 12, 75 (1974). ADS, Google Scholar
4. G. Parisi, Phys. Rep. 49, 215 (1979). Web of Science, ADS, Google Scholar
5. J. Ecalle, Les Fonctions Résurgentes, 3 volumes, Publications Mathématiques d’Orsay (1981). Google Scholar
6. A. Maiezza and J. C. Vasquez, Ann. Phys. 407, 78 (2019), arXiv:1902.05847. Web of Science, ADS, Google Scholar
7. J. Bersini, A. Maiezza and J. C. Vasquez, Ann. Phys. 415, 168126 (2020), arXiv:1910.14507. Web of Science, Google Scholar
8. J. Écalle, Six lectures on transseries, analysable functions and the constructive proof of dulac’s conjecture, in Bifurcations and Periodic Orbits of Vector Fields, NATO ASI Ser., Vol. 408 (Springer, 1993). Google Scholar
9. O. Costin, Int. Math. Res. Not. 1995, 377 (1995). Google Scholar
10. D. Dorigoni, An introduction to resurgence, trans-series and alien calculus, arXiv:1411.3585. Google Scholar
11. G. V. Dunne and M. Unsal, Annu. Rev. Nucl. Part. Sci. 66, 245 (2016), arXiv:1601.03414. Web of Science, ADS, Google Scholar
12. I. Aniceto, G. Basar and R. Schiappa, Phys. Rep. 809, 1 (2019), arXiv:1802.10441. Web of Science, ADS, Google Scholar
13. O. Costin, Duke Math. J. 93, 289 (1998). Web of Science, Google Scholar
14. O. Costin, Asymptotics and Borel Summability (Monographs and Surveys in Pure and Applied Mathematics) (Chapman and Hall/CRC, 2008). Google Scholar
15. S.-K. Jian, E. Barnes and S. Das Sarma, Phys. Rev. Res. 2, 023310 (2020), arXiv:2003.05098. Google Scholar
16. G. Dvali, G. F. Giudice, C. Gomez and A. Kehagias, J. High Energy Phys. 08, 108 (2011), arXiv:1010.1415. Web of Science, ADS, Google Scholar
17. E. De Rafael and J. Rosner, Ann. Phys. 82, 369 (1974). Web of Science, ADS, Google Scholar
18. D. J. Broadhurst, Z. Phys. C 58, 339 (1993). ADS, Google Scholar
19. L. Klaczynski and D. Kreimer, Ann. Phys. 344, 213 (2014), arXiv:1309.5061. Web of Science, ADS, Google Scholar
20. M. E. Peskin and D. V. Schroeder, An Introduction to Quantum Field Theory (Addison-Wesley, Reading, 1995). Google Scholar
21. M. P. Bellon and P. J. Clavier, Lett. Math. Phys. 109, 2003 (2019), arXiv:1806.08254. Web of Science, ADS, Google Scholar
22. M. P. Bellon and P. J. Clavier, Lett. Math. Phys. 105, 795 (2015), arXiv:1411.7190. Web of Science, ADS, Google Scholar
23. M. Borinsky and G. V. Dunne, Non-perturbative completion of Hopf-algebraic Dyson-Schwinger equations, arXiv:2005.04265. Google Scholar
24. P. J. Clavier, Borel-Ecalle resummation of a two-point function, arXiv:1912.03237. Google Scholar
25. E. Gardi and G. Grunberg, Phys. Lett. B 517, 215 (2001), arXiv:hep-ph/0107300. Web of Science, ADS, Google Scholar
26. K. G. Wilson and J. Kogut, Phys. Rep. 12, 75 (1974). ADS, Google Scholar
27. R. Haag, Kong. Dan. Vid. Sel. Mat. Fys. Med. 29, 1 (1955). Google Scholar
28. L. Klaczynski, Haag’s theorem in renormalised quantum field theories, Ph.D. thesis, Humboldt University, Berlin, 2016, arXiv:1602.00662. https://doi.org/10.18452/17448 Google Scholar
29. P. Argyres and M. Unsal, Phys. Rev. Lett. 109, 121601 (2012), arXiv:1204.1661. Web of Science, ADS, Google Scholar
30. G. Altarelli, Introduction to renormalons, in 5th Hellenic School and Workshops on Elementary Particle Physics (1996), pp. 221–236. Google Scholar
31. V. I. Zakharov, Prog. Theor. Phys. Suppl. 131, 107 (1998), arXiv:hep-ph/9802416. ADS, Google Scholar
32. M. Beneke, Phys. Rep. 317, 1 (1999), arXiv:hep-ph/9807443. Web of Science, ADS, Google Scholar
33. M. Shifman, Int. J. Mod. Phys. A 30, 1543001 (2015), arXiv:1310.1966. Link, Web of Science, ADS, Google Scholar
34. M. P. Bellon and P. J. Clavier, Lett. Math. Phys. 108, 391 (2018), arXiv:1612.07813. Web of Science, ADS, Google Scholar
35. G. ’t Hooft, Nucl. Phys. B (Proc. Suppl.) 121, 333 (2003), arXiv:hep-th/0207179. Web of Science, ADS, Google Scholar
36. G. Parisi, On non-renormalizable interactions, in New Developments in Quantum Field Theory and Statistical Mechanics, Cargèse, 1976 (Springer, 1977), pp. 281–305. https://doi.org/10.1007/978-1-4615-8918-1˙12 Google Scholar
37. H. Mera, T. G. Pedersen and B. K. Nikolić, Phys. Rev. D 97, 105027 (2018), arXiv:1802.06034. Web of Science, ADS, Google Scholar
38. O. Antipin, A. Maiezza and J. Carlos Vasquez, Nucl. Phys. B 941, 72 (2019), arXiv:1807.05060. Web of Science, ADS, Google Scholar
39. G. Grunberg, Phys. Rev. D 29, 2315 (1984). Web of Science, ADS, Google Scholar
40. M. Beneke, Phys. Lett. B 307, 154 (1993). Web of Science, ADS, Google Scholar
41. K. G. Wilson, Phys. Rev. 179, 1499 (1969). Web of Science, ADS, Google Scholar
42. G. Dvali, Subnucl. Ser. 53, 189 (2017), arXiv:1607.07422. Google Scholar
43. I. Crutchfield and Y. William, Phys. Lett. B 91, 425 (1980). Web of Science, ADS, Google Scholar