Critical Points at Infinity, Non-Gaussian Saddles, and Bions

Behtash, Alireza; Dunne, Gerald V.; Schaefer, Thomas; Sulejmanpasic, Tin; Ünsal, Mithat

doi:10.1007/JHEP06(2018)068

Critical Points at Infinity, Non-Gaussian Saddles, and Bions

Alireza Behtash
(
- Santa Barbara, KITP and
- North Carolina State U.
)
,
Gerald V. Dunne
(
- Santa Barbara, KITP and
- Connecticut U.
)
,
Thomas Schaefer
(
- North Carolina State U.
)
,
Tin Sulejmanpasic
(
- Santa Barbara, KITP and
- ENS, Paris, IPM
)
,
Mithat Ünsal
(
- Santa Barbara, KITP and
- North Carolina State U.
)

Mar 30, 2018

30 pages

Published in:

JHEP 06 (2018) 068

Published: Jun 13, 2018

e-Print:

1803.11533 [hep-th]

DOI:

10.1007/JHEP06(2018)068

Report number:

NSF-ITP-18-007

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Abstract: (Springer)

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

\left[\mathrm{\mathcal{I}}\overline{\mathrm{\mathcal{I}}}\right]

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

\left[\mathrm{\mathcal{I}}\overline{\mathrm{\mathcal{I}}}\right]

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.

Note:

31 pages, v2: fixed hyperlinks to references, minor edits

Nonperturbative Effects
Differential and Algebraic Geometry
Resummation
potential: quantum
boson: potential
critical phenomena
field theory
non-Gaussianity
quantum mechanics
nonperturbative

References(60)

Figures(6)

[1]

Aspects of Symmetry. Cambridge University Press

S.R. Coleman

[2]

Quantum field theory and critical phenomena

Jean Zinn-Justin
(
- Saclay
)

- Int.Ser.Monogr.Phys. 113 (2002) 1-1054

[3]

CALCULATION OF INSTANTON - ANTI-INSTANTON CONTRIBUTIONS IN QUANTUM MECHANICS

E.B. Bogomolny
(
- Landau Inst.
)

- Phys.Lett.B 91 (1980) 431-435,
- In *Le Guillou, J.C. (ed.), Zinn-Justin, J. (ed.): Large-order behaviour of perturbation theory* 175-179. (Phys. Lett. B91 (1980) 431-435). (see Book Index)
•
DOI:
- 10.1016/0370-2693(80)91014-X

[4]

Multi - Instanton Contributions in Quantum Mechanics

Jean Zinn-Justin
(
- Saclay
)

- Nucl.Phys.B 192 (1981) 125-140,
- In *Le Guillou, J.C. (ed.), Zinn-Justin, J. (ed.): Large-order behaviour of perturbation theory* 190-205. (Nucl. Phys. B192 (1981) 125-140) and Saclay CEN - D.PH.T-81-034 (81,rec.Jul.) 22 p. (see Book Index)
•
DOI:
- 10.1016/0550-3213(81)90197-8