Critical points at infinity, non-Gaussian saddles, and bions

Journal Article · Wed Jun 13 00:00:00 EDT 2018 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep06(2018)068· OSTI ID:1507776

Behtash, Alireza ^[1]; Dunne, Gerald V. ^[2]; Schäfer, Thomas ^[3]; Sulejmanpasic, Tin ^[4]; Ünsal, Mithat ^[1]

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1. Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics; Univ. of North Carolina, Raleigh, NC (United States). Dept. of Physics
2. Univ. of California, Santa Barbara, CA (United States). Kavli Inst. for Theoretical Physics; Univ. of Connecticut, Storrs, CT (United States). Dept. of Physics
3. Univ. of North Carolina, Raleigh, NC (United States). Dept. of Physics
4. 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 Berlin
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Nonperturbative Effects
Differential and Algebraic Geometry
Resummation