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

Abstract

We study the dynamics of four dimensional gauge theories with adjoint fermions for all gauge groups, both in perturbation theory and non-perturbatively, by using circle compactification with periodic boundary conditions for the fermions. There are new gauge phenomena. We show that, to all orders in perturbation theory, many gauge groups are Higgsed by the gauge holonomy around the circle to a product of both abelian and nonabelian gauge group factors. Non-perturbatively there are monopole-instantons with fermion zero modes and two types of monopole-anti-monopole molecules, called bions. One type are magnetic bions which carry net magnetic charge and induce a mass gap for gauge fluctuations. Another type are neutral bions which are magnetically neutral, and their understanding requires a generalization of multi-instanton techniques in quantum mechanics — which we refer to as the Bogomolny-Zinn-Justin (BZJ) prescription — to compactified field theory. The BZJ prescription applied to bion-anti-bion topological molecules predicts a singularity on the positive real axis of the Borel plane (i.e., a divergence from summing large orders in peturbation theory) which is of order N times closer to the origin than the leading 4-d BPST instanton-anti-instanton singularity, where N is the rank of the gauge group. The position of themore » bion-anti-bion singularity is thus qualitatively similar to that of the 4-d IR renormalon singularity, and we conjecture that they are continuously related as the compactification radius is changed. By making use of transseries and Écalle’s resurgence theory we argue that a non-perturbative continuum definition of a class of field theories which admit semi-classical expansions may be possible.« less

Authors:
 [1];  [2]
  1. Univ. of Cincinnati, OH (United States)
  2. San Francisco State Univ., CA (United States). Dept Physics & Astronomy; SLAC National Accelerator Lab., Menlo Park, CA (United States)
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), High Energy Physics (HEP)
OSTI Identifier:
1362077
Report Number(s):
SLAC-PUB-16996
Journal ID: ISSN 1029-8479; arXiv:1206.1890
Grant/Contract Number:  
AC02-76SF00515
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: 2012; Journal Issue: 8; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; Theory-HEP; ASTRO; HEPTH

Citation Formats

Argyres, Philip C., and Uensal, Mithat. The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects. United States: N. p., 2012. Web. doi:10.1007/JHEP08(2012)063.
Argyres, Philip C., & Uensal, Mithat. The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects. United States. doi:10.1007/JHEP08(2012)063.
Argyres, Philip C., and Uensal, Mithat. Fri . "The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects". United States. doi:10.1007/JHEP08(2012)063. https://www.osti.gov/servlets/purl/1362077.
@article{osti_1362077,
title = {The semi-classical expansion and resurgence in gauge theories: new perturbative, instanton, bion, and renormalon effects},
author = {Argyres, Philip C. and Uensal, Mithat},
abstractNote = {We study the dynamics of four dimensional gauge theories with adjoint fermions for all gauge groups, both in perturbation theory and non-perturbatively, by using circle compactification with periodic boundary conditions for the fermions. There are new gauge phenomena. We show that, to all orders in perturbation theory, many gauge groups are Higgsed by the gauge holonomy around the circle to a product of both abelian and nonabelian gauge group factors. Non-perturbatively there are monopole-instantons with fermion zero modes and two types of monopole-anti-monopole molecules, called bions. One type are magnetic bions which carry net magnetic charge and induce a mass gap for gauge fluctuations. Another type are neutral bions which are magnetically neutral, and their understanding requires a generalization of multi-instanton techniques in quantum mechanics — which we refer to as the Bogomolny-Zinn-Justin (BZJ) prescription — to compactified field theory. The BZJ prescription applied to bion-anti-bion topological molecules predicts a singularity on the positive real axis of the Borel plane (i.e., a divergence from summing large orders in peturbation theory) which is of order N times closer to the origin than the leading 4-d BPST instanton-anti-instanton singularity, where N is the rank of the gauge group. The position of the bion-anti-bion singularity is thus qualitatively similar to that of the 4-d IR renormalon singularity, and we conjecture that they are continuously related as the compactification radius is changed. By making use of transseries and Écalle’s resurgence theory we argue that a non-perturbative continuum definition of a class of field theories which admit semi-classical expansions may be possible.},
doi = {10.1007/JHEP08(2012)063},
journal = {Journal of High Energy Physics (Online)},
number = 8,
volume = 2012,
place = {United States},
year = {2012},
month = {8}
}

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Works referenced in this record:

Quantised Singularities in the Electromagnetic Field
journal, September 1931

  • Dirac, P. A. M.
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 133, Issue 821
  • DOI: 10.1098/rspa.1931.0130

Renormalons
journal, August 1999


Abelian Duality, Confinement, and Chiral-Symmetry Breaking in a SU(2) QCD-Like Theory
journal, January 2008


Gauge theories and magnetic charge
journal, July 1977


Constituent monopoles through the eyes of fermion zero-modes
journal, August 2003


The large N limit of four dimensional Yang-Mills field coupled to adjoint fermions on a single site lattice
journal, January 2010


Quark confinement and topology of gauge theories
journal, March 1977


Multi-instanton contributions in quantum mechanics
journal, November 1981


Nonperturbative effects and the large-order behavior of matrix models and topological strings
journal, January 2008

  • Mariño, Marcos; Schiappa, Ricardo; Weiss, Marlene
  • Communications in Number Theory and Physics, Vol. 2, Issue 2
  • DOI: 10.4310/CNTP.2008.v2.n2.a3

Volume independence in large N c QCD-like gauge theories
journal, June 2007


Large order calculations in gauge theories
journal, November 1977


Monopole constituents inside SU(n) calorons
journal, September 1998


Constraints on supersymmetry breaking
journal, July 1982


Borel and Stokes Nonperturbative Phenomena in Topological String Theory and c = 1 Matrix Models
journal, June 2010


On the phase transition towards permanent quark confinement
journal, June 1978


How instantons solve the U(1) problem
journal, September 1986


QCD and instantons at finite temperature
journal, January 1981

  • Gross, David J.; Pisarski, Robert D.; Yaffe, Laurence G.
  • Reviews of Modern Physics, Vol. 53, Issue 1
  • DOI: 10.1103/RevModPhys.53.43

Nonperturbative effects and nonperturbative definitions in matrix models and topological strings
journal, December 2008


k-string tension from Eguchi-Kawai reduction
journal, October 2011

  • Armoni, Adi; Dorigoni, Daniele; Veneziano, Gabriele
  • Journal of High Energy Physics, Vol. 2011, Issue 10
  • DOI: 10.1007/JHEP10(2011)086

Geometric engineering of N = 1 quantum field theories
journal, July 1997


Reduction of Dynamical Degrees of Freedom in the Large- N Gauge Theory
journal, April 1982


A note on perturbation series in supersymmetric gauge theories
journal, June 2012


Adjoint fermion zero-modes for SU( N ) calorons
journal, June 2009

  • Pérez, Margarita García; González-Arroyo, Antonio; Sastre, Alfonso
  • Journal of High Energy Physics, Vol. 2009, Issue 06
  • DOI: 10.1088/1126-6708/2009/06/065

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


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


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


Microscopic structure of magnetic bions
journal, June 2011

  • Anber, Mohamed M.; Poppitz, Erich
  • Journal of High Energy Physics, Vol. 2011, Issue 6
  • DOI: 10.1007/JHEP06(2011)136

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


Exact results in non-supersymmetric large N orientifold field theories
journal, September 2003


An L2-Index Theorem for Dirac Operators on S1×R3
journal, October 2000

  • Nye, Tom M. W.; Singer, Michael A.
  • Journal of Functional Analysis, Vol. 177, Issue 1
  • DOI: 10.1006/jfan.2000.3648

Hyperasymptotics for Integrals with Saddles
journal, September 1991

  • Berry, M. V.; Howls, C. J.
  • Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 434, Issue 1892
  • DOI: 10.1098/rspa.1991.0119

Monopoles, affine algebras and the gluino condensate
journal, August 2003

  • Davies, N. Michael; Hollowood, Timothy J.; Khoze, Valentin V.
  • Journal of Mathematical Physics, Vol. 44, Issue 8
  • DOI: 10.1063/1.1586477

Instanton vacuum in supersymmetric QCD
journal, February 1988


Dynamics of non-integrable phases and gauge symmetry breaking
journal, March 1989


Instantons and (super-) symmetry breaking in (2+1) dimensions
journal, October 1982


Anharmonic Oscillator
journal, August 1969


Premiers pas en calcul étranger
journal, January 1993

  • Candelpergher, B.; Nosmas, Jean-Claude; Pham, Frédéric
  • Annales de l’institut Fourier, Vol. 43, Issue 1
  • DOI: 10.5802/aif.1327

Index theorem for topological excitations on R 3 × S 1 and Chern-Simons theory
journal, March 2009


Collective-coordinate method for quasizero modes
journal, February 1986


    Works referencing / citing this record:

    Uniform WKB, multi-instantons, and resurgent trans-series
    journal, May 2014


    The renormalon diagram in gauge theories on ℝ 3 × S 1 $$ {\mathrm{\mathbb{R}}}^3\times {\mathbb{S}}^1 $$
    journal, January 2015

    • Anber, Mohamed M.; Sulejmanpasic, Tin
    • Journal of High Energy Physics, Vol. 2015, Issue 1
    • DOI: 10.1007/jhep01(2015)139

    Resurgence and the Nekrasov-Shatashvili limit: connecting weak and strong coupling in the Mathieu and Lamé systems
    journal, February 2015


    Geometric constraints on the space of N $$ \mathcal{N} $$ = 2 SCFTs. Part II: construction of special Kähler geometries and RG flows
    journal, February 2018

    • Argyres, Philip C.; Lotito, Matteo; Lü, Yongchao
    • Journal of High Energy Physics, Vol. 2018, Issue 2
    • DOI: 10.1007/jhep02(2018)002

    Bion non-perturbative contributions versus infrared renormalons in two-dimensional ℂPN − 1 models
    journal, February 2019

    • Fujimori, Toshiaki; Kamata, Syo; Misumi, Tatsuhiro
    • Journal of High Energy Physics, Vol. 2019, Issue 2
    • DOI: 10.1007/jhep02(2019)190

    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

    New nonperturbative scales and glueballs in confining supersymmetric gauge theories
    journal, March 2018

    • Anber, Mohamed M.; Poppitz, Erich
    • Journal of High Energy Physics, Vol. 2018, Issue 3
    • DOI: 10.1007/jhep03(2018)052

    Fractional instanton of the SU(3) gauge theory in weak coupling regime
    journal, May 2019


    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

    Adjoint QCD on ℝ3 × S 1 with twisted fermionic boundary conditions
    journal, June 2014

    • Misumi, Tatsuhiro; Kanazawa, Takuya
    • Journal of High Energy Physics, Vol. 2014, Issue 6
    • DOI: 10.1007/jhep06(2014)181

    Vacuum structure of bifundamental gauge theories at finite topological angles
    journal, June 2017


    From 4d Yang-Mills to 2d ℂℙN − 1 model: IR problem and confinement at weak coupling
    journal, July 2017

    • Yamazaki, Masahito; Yonekura, Kazuya
    • Journal of High Energy Physics, Vol. 2017, Issue 7
    • DOI: 10.1007/jhep07(2017)088

    Quantum distillation of Hilbert spaces, semi-classics and anomaly matching
    journal, August 2018

    • Dunne, Gerald V.; Tanizaki, Yuya; Ünsal, Mithat
    • Journal of High Energy Physics, Vol. 2018, Issue 8
    • DOI: 10.1007/jhep08(2018)068

    Renormalons in quantum mechanics
    journal, August 2019

    • Pazarbası, Cihan; Van den Bleeken, Dieter
    • Journal of High Energy Physics, Vol. 2019, Issue 8
    • DOI: 10.1007/jhep08(2019)096

    Deconfinement and continuity between thermal and (super) Yang-Mills theory for all gauge groups
    journal, September 2014

    • Anber, Mohamed M.; Poppitz, Erich; Teeple, Brett
    • Journal of High Energy Physics, Vol. 2014, Issue 9
    • DOI: 10.1007/jhep09(2014)040

    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

    Resurgence and dynamics of O(N) and Grassmannian sigma models
    journal, September 2015


    Vacuum structure of Yang-Mills theory as a function of θ
    journal, September 2018

    • Aitken, Kyle; Cherman, Aleksey; Ünsal, Mithat
    • Journal of High Energy Physics, Vol. 2018, Issue 9
    • DOI: 10.1007/jhep09(2018)030

    On the global structure of deformed Yang-Mills theory and QCD(adj) on ℝ 3 × S 1 $$ {\mathrm{\mathbb{R}}}^3\times {\mathbb{S}}^1 $$
    journal, October 2015

    • Anber, Mohamed M.; Poppitz, Erich
    • Journal of High Energy Physics, Vol. 2015, Issue 10
    • DOI: 10.1007/jhep10(2015)051

    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

    Self-conjugate QCD
    journal, October 2019


    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

    Adiabatic continuity and confinement in supersymmetric Yang-Mills theory on the lattice
    journal, November 2018

    • Bergner, Georg; Piemonte, Stefano; Ünsal, Mithat
    • Journal of High Energy Physics, Vol. 2018, Issue 11
    • DOI: 10.1007/jhep11(2018)092

    Classification of compactified su(Nc) gauge theories with fermions in all representations
    journal, December 2017

    • Anber, Mohamed M.; Vincent-Genod, Loïc
    • Journal of High Energy Physics, Vol. 2017, Issue 12
    • DOI: 10.1007/jhep12(2017)028

    Circle compactification and ’t Hooft anomaly
    journal, December 2017

    • Tanizaki, Yuya; Misumi, Tatsuhiro; Sakai, Norisuke
    • Journal of High Energy Physics, Vol. 2017, Issue 12
    • DOI: 10.1007/jhep12(2017)056

    Domain walls and deconfinement: a semiclassical picture of discrete anomaly inflow
    journal, December 2019

    • Cox, Andrew A.; Poppitz, Erich; Wong, Samuel S. Y.
    • Journal of High Energy Physics, Vol. 2019, Issue 12
    • DOI: 10.1007/jhep12(2019)011

    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

    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

    Infrared renormalon in the supersymmetric $\mathbb{C}P^{N-1}$ model on $\mathbb{R}\times S^1$
    journal, February 2020

    • Ishikawa, Kosuke; Morikawa, Okuto; Nakayama, Akira
    • Progress of Theoretical and Experimental Physics, Vol. 2020, Issue 2
    • DOI: 10.1093/ptep/ptaa002

    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

    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

    Dihedral symmetry in S U ( N ) Yang-Mills theory
    journal, October 2019


    Flow of Hagedorn singularities and phase transitions in large N gauge theories
    journal, January 2020


    Theta dependence, sign problems, and topological interference
    journal, November 2012


    Continuity and Resurgence: Towards a continuum definition of the C P ( N 1 ) model
    journal, January 2013


    Strings from domain walls in supersymmetric Yang-Mills theory and adjoint QCD
    journal, July 2015


    Nonperturbative contributions from complexified solutions in C P N 1 models
    journal, November 2016


    Entropy production, hydrodynamics, and resurgence in the primordial quark-gluon plasma from holography
    journal, November 2016


    QCD on a small circle
    journal, November 2017


    Hyperasymptotics and quark-hadron duality violations in QCD
    journal, March 2018


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


    Hydrodynamics Beyond the Gradient Expansion: Resurgence and Resummation
    journal, August 2015


    Global Symmetries, Volume Independence, and Continuity in Quantum Field Theories
    journal, January 2017


    The grin of Cheshire cat resurgence from supersymmetric localization
    journal, January 2018


    Determining $\alpha_s$ from hadronic $\tau$ decay: the pitfalls of truncating the OPE
    journal, January 2019