Critical points at infinity, non-Gaussian saddles, and bions
- Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics; Univ. of North Carolina, Raleigh, NC (United States). Dept. of Physics
- Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics; Univ. of Connecticut, Storrs, CT (United States). Dept. of Physics
- Univ. of North Carolina, Raleigh, NC (United States). Dept. of Physics
- Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics; PSL Research Univ., Paris (France). Philippe Meyer Inst., Physics Dept.
It has been argued that many non-perturbative phenomena in quantum mechanics (QM) and quantum field theory (QFT) are determined by complex field configurations, and that these contributions should be understood in terms of Picard-Lefschetz theory. In this work we compute the contribution from non-BPS multi-instanton configurations, such as instanton-anti-instanton [$$I\overline{I}$$] pairs, and argue that these contributions should be interpreted as exact critical points at infinity. The Lefschetz thimbles associated with such critical points have a specific structure arising from the presence of non-Gaussian, quasi-zero mode (QZM), directions. When fermion degrees of freedom are present, as in supersymmetric theories, the effective bosonic potential can be written as the sum of a classical and a quantum potential. We show that in this case the semi-classical contribution of the critical point at infinity vanishes, but there is a non-trivial contribution that arises from its associated non-Gaussian QZM-thimble. This approach resolves several puzzles in the literature concerning the semi-classical contribution of correlated [$$I\overline{I}$$] pairs. It has the surprising consequence that the configurations dominating the expansion of observables, and the critical points defining the Lefschetz thimble decomposition need not be the same, a feature not present in the traditional Picard-Lefschetz approach.
- Research Organization:
- North Carolina State University, Raleigh, NC (United States); Univ. of Connecticut, Storrs, CT (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), High Energy Physics (HEP); USDOE Office of Science (SC), Nuclear Physics (NP)
- Grant/Contract Number:
- FG02-03ER41260; SC0010339
- OSTI ID:
- 1507776
- Journal Information:
- Journal of High Energy Physics (Online), Vol. 2018, Issue 6; ISSN 1029-8479
- Publisher:
- Springer BerlinCopyright Statement
- Country of Publication:
- United States
- Language:
- English
Web of Science
Instantons in the Hofstadter butterfly: difference equation, resurgence and quantum mirror curves
|
journal | January 2019 |
Instantons in the Hofstadter butterfly: difference equation, resurgence and quantum mirror curves | text | January 2018 |
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