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

Abstract

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.

Authors:
 [1];  [2];  [1];  [1]
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  1. North Carolina State Univ., Raleigh, NC (United States). Dept. of Physics
  2. Univ. of Toronto, Toronto, ON (Canada). Dept. of Physics
Publication Date:
Research Org.:
North Carolina State University, Raleigh, NC (United States); Univ. of Toronto, Toronto, ON (Canada)
Sponsoring Org.:
USDOE Office of Science (SC), Nuclear Physics (NP); Natural Sciences and Engineering Research Council of Canada (NSERC)
OSTI Identifier:
1436879
Grant/Contract Number:  
SC0013036
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2015; Journal Issue: 11; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; solitons monopoles and instantons; nonperturbative effects; extended supersymmetry

Citation Formats

Behtash, Alireza, Poppitz, Erich, Sulejmanpasic, Tin, and Unsal, Mithat. The curious incident of multi-instantons and the necessity of Lefschetz thimbles. United States: N. p., 2015. Web. doi:10.1007/JHEP11(2015)175.
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Behtash, Alireza, Poppitz, Erich, Sulejmanpasic, Tin, & Unsal, Mithat. The curious incident of multi-instantons and the necessity of Lefschetz thimbles. United States. https://doi.org/10.1007/JHEP11(2015)175
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Behtash, Alireza, Poppitz, Erich, Sulejmanpasic, Tin, and Unsal, Mithat. Wed . "The curious incident of multi-instantons and the necessity of Lefschetz thimbles". United States. https://doi.org/10.1007/JHEP11(2015)175. https://www.osti.gov/servlets/purl/1436879.
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@article{osti_1436879,
title = {The curious incident of multi-instantons and the necessity of Lefschetz thimbles},
author = {Behtash, Alireza and Poppitz, Erich and Sulejmanpasic, Tin and Unsal, Mithat},
abstractNote = {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.},
doi = {10.1007/JHEP11(2015)175},
journal = {Journal of High Energy Physics (Online)},
number = 11,
volume = 2015,
place = {United States},
year = {Wed Nov 25 00:00:00 EST 2015},
month = {Wed Nov 25 00:00:00 EST 2015}
}
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Journal Article:
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Publisher's Version of Record
https://doi.org/10.1007/JHEP11(2015)175
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Cited by: 28 works
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Figures / Tables:

Figure 1 Figure 1: Top: a fermion-correlatedmore » $I$$\bar{I}$ event, contributing the rst term in eq. (2.8). Bottom: a scalar-correlated $I$$\bar{I}$ event, contributing the second term in eq. (2.8). The two contributions are proportional to different powers of the perturbative (g $\ll$ ω3) coupling g. In QM, the diagrams are intended to schematically represent the lifting of fermion zero modes by the two mechanisms. In QFT, one can associate the (anti-)instanton vertices with effective 't Hooft interactions and the lines connecting them to free (away from the instanton cores) scalar and fermion propagators.« less
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Works referenced in this record:

Hidden Topological Angles in Path Integrals
journal, July 2015

Resurgence theory, ghost-instantons, and analytic continuation of path integrals
journal, October 2013

  • Basar, Gökçe; Dunne, Gerald V.; Ünsal, Mithat
  • Journal of High Energy Physics, Vol. 2013, Issue 10
  • DOI: 10.1007/JHEP10(2013)041

Continuity, deconfinement, and (super) Yang-Mills theory
journal, October 2012

  • Poppitz, Erich; Schäfer, Thomas; Ünsal, Mithat
  • Journal of High Energy Physics, Vol. 2012, Issue 10
  • DOI: 10.1007/JHEP10(2012)115

Classifying bions in Grassmann sigma models and non-Abelian gauge theories by D-branes
journal, March 2015

  • Misumi, Tatsuhiro; Nitta, Muneto; Sakai, Norisuke
  • Progress of Theoretical and Experimental Physics, Vol. 2015, Issue 3
  • DOI: 10.1093/ptep/ptv009

Quark confinement and topology of gauge theories
journal, March 1977

Multi-instanton contributions in quantum mechanics
journal, November 1981

Structure of Lefschetz thimbles in simple fermionic systems
journal, March 2015

Resurgence and trans-series in Quantum Field Theory: the $\mathbb{C}{{\mathbb{P}}^{N-1 }}$ model
journal, November 2012

  • Dunne, Gerald V.; Ünsal, Mithat
  • Journal of High Energy Physics, Vol. 2012, Issue 11
  • DOI: 10.1007/JHEP11(2012)170

Nonperturbative Ambiguities and the Reality of Resurgent Transseries
journal, October 2014

Instantons in QCD
journal, April 1998

Ground state structure in supersymmetric quantum mechanics
journal, September 1987

The resurgence of instantons in string theory
journal, January 2012

  • Aniceto, Inês; Schiappa, Ricardo; Vonk, Marcel
  • Communications in Number Theory and Physics, Vol. 6, Issue 2
  • DOI: 10.4310/CNTP.2012.v6.n2.a3

Resurgence in Quantum Field Theory: Nonperturbative Effects in the Principal Chiral Model
journal, January 2014

Neutral bions in the CP N-1 model for resurgence
journal, April 2015

Analytic continuation of Chern-Simons theory
book, January 2010

Analytic continuation of Liouville theory
journal, December 2011

  • Harlow, Daniel; Maltz, Jonathan; Witten, Edward
  • Journal of High Energy Physics, Vol. 2011, Issue 12
  • DOI: 10.1007/JHEP12(2011)071

The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects
journal, August 2012

  • Argyres, Philip C.; Ünsal, Mithat
  • Journal of High Energy Physics, Vol. 2012, Issue 8
  • DOI: 10.1007/JHEP08(2012)063

Neutral bions in the ℂ $$ \mathbb{C} $$ P N −1 model
journal, June 2014

  • Misumi, Tatsuhiro; Nitta, Muneto; Sakai, Norisuke
  • Journal of High Energy Physics, Vol. 2014, Issue 6
  • DOI: 10.1007/JHEP06(2014)164

Universal mechanism of (semi-classical) deconfinement and θ-dependence for all simple groups
journal, March 2013

  • Poppitz, Erich; Schäfer, Thomas; Ünsal, Mithat
  • Journal of High Energy Physics, Vol. 2013, Issue 3
  • DOI: 10.1007/JHEP03(2013)087

Instanton molecular vacuum in N = 1 supersymmetric quantum mechanics
journal, September 1986

Seiberg-Witten and “Polyakov-like” magnetic bion confinements are continuously connected
journal, July 2011

Calculation of instanton-anti-instanton contributions in quantum mechanics
journal, April 1980

Three-loop correction to the instanton density. II. The sine-Gordon potential
journal, July 2015

(S)QCD on $ {{\mathbb{R}}^3}\times {{\mathbb{S}}^1} $ : screening of Polyakov loop by fundamental quarks and the demise of semi-classics
journal, September 2013

  • Poppitz, Erich; Sulejmanpasic, Tin
  • Journal of High Energy Physics, Vol. 2013, Issue 9
  • DOI: 10.1007/JHEP09(2013)128

Three-loop correction to the instanton density. I. The quartic double well potential
journal, July 2015

Resurgence in sine-Gordon quantum mechanics: exact agreement between multi-instantons and uniform WKB
journal, September 2015

  • Misumi, Tatsuhiro; Nitta, Muneto; Sakai, Norisuke
  • Journal of High Energy Physics, Vol. 2015, Issue 9
  • DOI: 10.1007/JHEP09(2015)157

Multi-instanton contributions in quantum mechanics (II)
journal, June 1983

Instanton vacuum in supersymmetric QCD
journal, February 1988

Holonomy potential and confinement from a simple model of the gauge topology
journal, October 2013

Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles
journal, October 2015

  • Cherman, Aleksey; Dorigoni, Daniele; Ünsal, Mithat
  • Journal of High Energy Physics, Vol. 2015, Issue 10
  • DOI: 10.1007/JHEP10(2015)056

Collective-coordinate method for quasizero modes
journal, February 1986

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    Works referencing / citing this record:

    Instantons in the Hofstadter butterfly: difference equation, resurgence and quantum mirror curves
    journal, January 2019

    • Duan, Zhihao; Gu, Jie; Hatsuda, Yasuyuki
    • Journal of High Energy Physics, Vol. 2019, Issue 1
    • DOI: 10.1007/jhep01(2019)079

    Cheshire Cat Resurgence, Self-Resurgence and Quasi-Exact Solvable Systems
    journal, October 2018

    • Kozçaz, Can; Sulejmanpasic, Tin; Tanizaki, Yuya
    • Communications in Mathematical Physics, Vol. 364, Issue 3
    • DOI: 10.1007/s00220-018-3281-y
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