Spectral flow in instanton computations and the β functions

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We discuss various differences in the instanton-based calculations of the β functions in theories such as Yang-Mills and CP(N-1) on one hand, and λφ4 theory with Symanzik's sign-reversed prescription for the coupling constant λ on the other hand. Although the aforementioned theories are asymptotically free, in the first two theories, instantons are topological, whereas the Fubini-Lipatov instanton in the third theory is topologically trivial. The spectral structure in the background of the Fubini-Lipatov instanton can be continuously deformed into that in the flat background, establishing a one-to-one correspondence between the two spectra. However, when considering topologically nontrivial backgrounds for Yang-Mills and CP(N-1) theories, the spectrum undergoes restructuring. In these cases, a mismatch between the spectra around the instanton and the trivial vacuum occurs.

Original languageEnglish (US)
Article number105002
JournalPhysical Review D
Issue number10
StatePublished - Nov 15 2023

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© 2023 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.


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