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Title: Bion non-perturbative contributions versus infrared renormalons in two-dimensional $$\mathbb{C}$$PN - 1 models

Abstract

We derive the semiclassical contributions from the real and complex bions in the two-dimensional $$\mathbb{C}$$PN 1 sigma model on $$\mathbb{R}$$×S1 with a twisted boundary condition. The bion configurations are saddle points of the complexified Euclidean action, which can be viewed as bound states of a pair of fractional instantons with opposite topological charges. We first derive the bion solutions by solving the equation of motion in the model with a potential which simulates an interaction induced by fermions in the $$\mathbb{C}$$PN - 1 quantum mechanics. The bion solutions have quasi-moduli parameters corresponding to the relative distance and phase between the constituent fractional instantons. By summing over the Kaluza-Klein modes of the quantum fluctuations around the bion backgrounds, we find that the effective action for the quasi-moduli parameters is renormalized and becomes a function of the dynamical scale (or the renormalized coupling constant). Based on the renormalized effective action, we obtain the semiclassical bion contribution in a weak coupling limit by making use of the Lefschetz thimble method. We find in the supersymmetric case that the bion contribution vanishes as expected from supersymmetry. In non-supersymmetric cases, the non-perturbative contribution has an imaginary ambiguity which is consistent with the expected infrared renormalon ambiguity. Our results explicitly demonstrate that the complex bion can explain the infrared renormalon.

Authors:
 [1];  [2];  [3];  [1];  [1]
+ Show Author Affiliations
  1. Keio Univ., Kanagawa (Japan)
  2. North Carolina State Univ., Raleigh, NC (United States)
  3. Keio Univ., Kanagawa (Japan); Akita Univ. (Japan); Inst. of Physical and Chemical Research (RIKEN), Wako (Japan)
Publication Date:
Research Org.:
North Carolina State University, Raleigh, NC (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1609452
Grant/Contract Number:  
FG02-03ER41260
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: 2019; Journal Issue: 2; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
73 NUCLEAR PHYSICS AND RADIATION PHYSICS; Physics

Citation Formats

Fujimori, Toshiaki, Kamata, Syo, Misumi, Tatsuhiro, Nitta, Muneto, and Sakai, Norisuke. Bion non-perturbative contributions versus infrared renormalons in two-dimensional $\mathbb{C}$PN - 1 models. United States: N. p., 2019. Web. doi:10.1007/jhep02(2019)190.
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Fujimori, Toshiaki, Kamata, Syo, Misumi, Tatsuhiro, Nitta, Muneto, & Sakai, Norisuke. Bion non-perturbative contributions versus infrared renormalons in two-dimensional $\mathbb{C}$PN - 1 models. United States. https://doi.org/10.1007/jhep02(2019)190
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Fujimori, Toshiaki, Kamata, Syo, Misumi, Tatsuhiro, Nitta, Muneto, and Sakai, Norisuke. Wed . "Bion non-perturbative contributions versus infrared renormalons in two-dimensional $\mathbb{C}$PN - 1 models". United States. https://doi.org/10.1007/jhep02(2019)190. https://www.osti.gov/servlets/purl/1609452.
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@article{osti_1609452,
title = {Bion non-perturbative contributions versus infrared renormalons in two-dimensional $\mathbb{C}$PN - 1 models},
author = {Fujimori, Toshiaki and Kamata, Syo and Misumi, Tatsuhiro and Nitta, Muneto and Sakai, Norisuke},
abstractNote = {We derive the semiclassical contributions from the real and complex bions in the two-dimensional $\mathbb{C}$PN 1 sigma model on $\mathbb{R}$×S1 with a twisted boundary condition. The bion configurations are saddle points of the complexified Euclidean action, which can be viewed as bound states of a pair of fractional instantons with opposite topological charges. We first derive the bion solutions by solving the equation of motion in the model with a potential which simulates an interaction induced by fermions in the $\mathbb{C}$PN - 1 quantum mechanics. The bion solutions have quasi-moduli parameters corresponding to the relative distance and phase between the constituent fractional instantons. By summing over the Kaluza-Klein modes of the quantum fluctuations around the bion backgrounds, we find that the effective action for the quasi-moduli parameters is renormalized and becomes a function of the dynamical scale (or the renormalized coupling constant). Based on the renormalized effective action, we obtain the semiclassical bion contribution in a weak coupling limit by making use of the Lefschetz thimble method. We find in the supersymmetric case that the bion contribution vanishes as expected from supersymmetry. In non-supersymmetric cases, the non-perturbative contribution has an imaginary ambiguity which is consistent with the expected infrared renormalon ambiguity. Our results explicitly demonstrate that the complex bion can explain the infrared renormalon.},
doi = {10.1007/jhep02(2019)190},
journal = {Journal of High Energy Physics (Online)},
number = 2,
volume = 2019,
place = {United States},
year = {Wed Feb 27 00:00:00 EST 2019},
month = {Wed Feb 27 00:00:00 EST 2019}
}
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text, January 2010

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preprint, January 2011

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text, January 2012

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text, January 2013

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Neutral bions in the CP^{N-1} model for resurgence
text, January 2014

Structure of Lefschetz thimbles in simple fermionic systems
text, January 2014

Resurgence of the Cusp Anomalous Dimension
text, January 2015

Exact quantization conditions for the relativistic Toda lattice
text, January 2015

Resurgence in $η$-deformed Principal Chiral Models
text, January 2016

Quantum Geometry of Resurgent Perturbative/Nonperturbative Relations
text, January 2017

Resurgence analysis of 2d Yang-Mills theory on a torus
text, January 2018

Kahler Normal Coordinate Expansion in Supersymmetric Theories
text, January 2000

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text, January 2002

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preprint, January 2006

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The background field method and the ultraviolet structure of the supersymmetric nonlinear σ-model
journal, April 1981

Valley instanton versus constrained instanton
journal, April 1996

Aspects of perturbation theory in quantum mechanics: The BenderWu Mathematica ® package
journal, July 2018

One-point functions of non-SUSY operators at arbitrary genus in a matrix model for type IIA superstrings
journal, June 2017

Conformality or confinement: (IR)relevance of topological excitations
journal, September 2009

Asymptotics of the Instantons of Painlevé I
journal, March 2011

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Complex instantons in sigma models with chemical potential
journal, September 2018

Resurgent functions and splitting problems
text, January 2007

Nonperturbative Effects and the Large-Order Behavior of Matrix Models and Topological Strings
preprint, January 2007

The Resurgence of Instantons in String Theory
preprint, January 2011

Monte Carlo simulations on the Lefschetz thimble: taming the sign problem
text, January 2013

Decoding perturbation theory using resurgence: Stokes phenomena, new saddle points and Lefschetz thimbles
preprint, January 2014

Classifying bions in Grassmann sigma models and non-Abelian gauge theories by D-branes
text, January 2014

Quantization conditions and functional equations in ABJ(M) theories
preprint, January 2014

Three-loop Correction to the Instanton Density. I. The Quartic Double Well Potential
text, January 2015

Hidden topological angles and Lefschetz thimbles
text, January 2015

Resurgence of the Cusp Anomalous Dimension
text, January 2015

Resurgence in sine-Gordon quantum mechanics: Exact agreement between multi-instantons and uniform WKB
text, January 2015

Exact quantization conditions for the relativistic Toda lattice
text, January 2015

Instantons from Perturbation Theory
text, January 2016

Valley Views: Instantons, Large Order Behaviors, and Supersymmetry
text, January 1998

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    Universal renormalons in principal chiral models
    text, January 2020

    Renormalon structure in compactified spacetime
    journal, January 2020

    • Ishikawa, Kosuke; Morikawa, Okuto; Shibata, Kazuya
    • Progress of Theoretical and Experimental Physics, Vol. 2020, Issue 1
    • DOI: 10.1093/ptep/ptz147

    Resurgence for superconductors
    journal, December 2019

    • Mariño, Marcos; Reis, Tomás
    • Journal of Statistical Mechanics: Theory and Experiment, Vol. 2019, Issue 12
    • DOI: 10.1088/1742-5468/ab4802

    Universal Renormalons in Principal Chiral Models
    text, January 2019

    Infrared renormalon in the supersymmetric $\mathbb{C}P^{N-1}$ model on $\mathbb{R}\times S^1$
    text, January 2019

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