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Title: The curious incident of multi-instantons and the necessity of Lefschetz thimbles

Journal Article · · Journal of High Energy Physics (Online)
 [1];  [2];  [1];  [1]
  1. North Carolina State Univ., Raleigh, NC (United States). Dept. of Physics
  2. Univ. of Toronto, Toronto, ON (Canada). Dept. of Physics
+ Show Author Affiliations

Here, we show that compatibility of supersymmetry with exact semi-classics demands that in calculating multi-instanton amplitudes, the “separation” quasi-zeromode must be complexified and the integration cycles must be found by using complex gradient flow (or Picard-Lefschetz equations.) As a non-trivial application, we study N = 2 extended supersymmetric quantum mechanics. Even though in this case supersymmetry is unbroken, the instanton-anti-instanton amplitude (naively calculated) seems to contribute to the ground state energy. We show, however, that the instanton-anti-instanton event consists of two parts: a fermion-correlated and a scalar-correlated event. Although both of these contributions are naively of the same sign and the latter is superficially higher order in the perturbative coupling, we show that the two contributions exactly cancel when they are evaluated on Lefschetz thimbles due to their relative Hidden Topological Angles (HTAs). This gives strong evidence that the semi-classical expansion using Lefschetz thimbles is not only a meaningful prescription for higher order semi-classics, but a necessary one. This deduction seems to be universal and applicable to both supersymmetric and non-supersymmetric theories. In conclusion we speculate that similar conspiracies are responsible for the non-formation of certain molecular contributions in theories where instantons have more than two fermionic zeromodes and do not contribute to the superpotential.

Research Organization:
North Carolina State University, Raleigh, NC (United States); Univ. of Toronto, Toronto, ON (Canada)
Sponsoring Organization:
USDOE Office of Science (SC), Nuclear Physics (NP); Natural Sciences and Engineering Research Council of Canada (NSERC)
Grant/Contract Number:
SC0013036
OSTI ID:
1436879
Journal Information:
Journal of High Energy Physics (Online), Vol. 2015, Issue 11; ISSN 1029-8479
Publisher:
Springer BerlinCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 28 works
Citation information provided by
Web of Science

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Cited By (5)

Instantons in the Hofstadter butterfly: difference equation, resurgence and quantum mirror curves journal January 2019
Cheshire Cat Resurgence, Self-Resurgence and Quasi-Exact Solvable Systems journal October 2018
Why is the mission impossible? Decoupling the mirror Ginsparg–Wilson fermions in the lattice models for two-dimensional Abelian chiral gauge theories journal July 2019
Why is the mission impossible? -- Decoupling the mirror Ginsparg-Wilson fermions in the lattice models for two-dimensional abelian chiral gauge theories text January 2017
Instantons in the Hofstadter butterfly: difference equation, resurgence and quantum mirror curves text January 2018

Figures / Tables (2)

Figure 1(p. 7)figure Figure 1
Figure 2(p. 9)figure Figure 2

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Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
solitons monopoles and instantons
nonperturbative effects
extended supersymmetry