Strongly coupled $\mathrm{QFT}$ dynamics via $\mathrm{TQFT}$ coupling

Ünsal, Mithat

doi:10.1007/jhep11(2021)134

Title: Strongly coupled $$\mathrm{QFT}$$ dynamics via $$\mathrm{TQFT}$$ coupling

Abstract

We consider a class of quantum field theories and quantum mechanics, which we couple to $$\mathbb{Z}$$_N topological QFTs, in order to classify non-perturbative effects in the original theory. The $$\mathbb{Z}$$_N TQFT structure arises naturally from turning on a classical background field for a $$\mathbb{Z}$$_N 0- or 1-form global symmetry. In SU(N) Yang-Mills theory coupled to $$\mathbb{Z}$$_N TQFT, the non-perturbative expansion parameter is exp[-S_I/N] = exp[-8π²/g²N] both in the semi-classical weak coupling domain and strong coupling domain, corresponding to a fractional topological charge configurations. To classify the non-perturbative effects in original SU(N) theory, we must use PSU(N) bundle and lift configurations (critical points at infinity) for which there is no obstruction back to SU(N). These provide a refinement of instanton sums: integer topological charge, but crucially fractional action configurations contribute, providing a TQFT protected generalization of resurgent semi-classical expansion to strong coupling. Monopole-instantons (or fractional instantons) on T³ x $$S^1_L$$ can be interpreted as tunneling events in the ’t Hooft flux background in the PSU(N) bundle. The construction provides a new perspective to the strong coupling regime of QFTs and resolves a number of old standing issues, especially, fixes the conflicts between the large-N and instanton analysis. We derive the mass gap at θ = 0 and gaplessness at θ = π in $$\mathbb{CP}$$¹ model, and mass gap for arbitrary θ in $$\mathbb{CP}$$ ^N-1, N ≥ 3 on $$\mathbb{R}$$².

Authors:

Ünsal, Mithat ^[1]

North Carolina State University, Raleigh, NC (United States)

Publication Date:: Thu Nov 18 00:00:00 EST 2021

Research Org.:: North Carolina State University, Raleigh, NC (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Nuclear Physics (NP)

OSTI Identifier:: 1976581

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: 2021; Journal Issue: 11; Journal ID: ISSN 1029-8479

Publisher:: Springer Nature

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; confinement; sigma models; solitons monopoles and instantons; topological field theories

Citation Formats


                    Ünsal, Mithat. Strongly coupled $\mathrm{QFT}$ dynamics via $\mathrm{TQFT}$ coupling.  United States: N. p., 2021. 
Web.  doi:10.1007/jhep11(2021)134.

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                    Ünsal, Mithat. Strongly coupled $\mathrm{QFT}$ dynamics via $\mathrm{TQFT}$ coupling.  United States.  https://doi.org/10.1007/jhep11(2021)134

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                    Ünsal, Mithat. Thu .  
"Strongly coupled $\mathrm{QFT}$ dynamics via $\mathrm{TQFT}$ coupling".  United States.  https://doi.org/10.1007/jhep11(2021)134.  https://www.osti.gov/servlets/purl/1976581.

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@article{osti_1976581,

  title        = {Strongly coupled $\mathrm{QFT}$ dynamics via $\mathrm{TQFT}$ coupling},

  author       = {Ünsal, Mithat},

  abstractNote = {We consider a class of quantum field theories and quantum mechanics, which we couple to $\mathbb{Z}$N topological QFTs, in order to classify non-perturbative effects in the original theory. The $\mathbb{Z}$N TQFT structure arises naturally from turning on a classical background field for a $\mathbb{Z}$N 0- or 1-form global symmetry. In SU(N) Yang-Mills theory coupled to $\mathbb{Z}$N TQFT, the non-perturbative expansion parameter is exp[-SI/N] = exp[-8π2/g2N] both in the semi-classical weak coupling domain and strong coupling domain, corresponding to a fractional topological charge configurations. To classify the non-perturbative effects in original SU(N) theory, we must use PSU(N) bundle and lift configurations (critical points at infinity) for which there is no obstruction back to SU(N). These provide a refinement of instanton sums: integer topological charge, but crucially fractional action configurations contribute, providing a TQFT protected generalization of resurgent semi-classical expansion to strong coupling. Monopole-instantons (or fractional instantons) on T3 x $S^1_L$ can be interpreted as tunneling events in the ’t Hooft flux background in the PSU(N) bundle. The construction provides a new perspective to the strong coupling regime of QFTs and resolves a number of old standing issues, especially, fixes the conflicts between the large-N and instanton analysis. We derive the mass gap at θ = 0 and gaplessness at θ = π in $\mathbb{CP}$1 model, and mass gap for arbitrary θ in $\mathbb{CP}$ N-1, N ≥ 3 on $\mathbb{R}$2.},

  doi          = {10.1007/jhep11(2021)134},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 11,

  volume       = 2021,

  place        = {United States},

  year         = {Thu Nov 18 00:00:00 EST 2021},

  month        = {Thu Nov 18 00:00:00 EST 2021}

}

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Title: Strongly coupled $$\mathrm{QFT}$$ dynamics via $$\mathrm{TQFT}$$ coupling

Abstract

Citation Formats

Field Theories of Condensed Matter Physics book, January 2013

The Confinement Problem in Lattice Gauge Theory text, January 2003

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Constraints on supersymmetry breaking journal, July 1982

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Instantons in the Higgs phase journal, July 2005

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

The topological objects near the chiral crossover transition in QCD journal, July 2019

Light quarks in the screened dyon-antidyon Coulomb liquid model. II. journal, October 2015

Confinement from Center Vortices: A review of old and new results journal, January 2017

Confining dyon-antidyon Coulomb liquid model. I. journal, October 2015

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

Semiclassical Realization of Infrared Renormalons journal, September 2012

Calorons on the lattice - a new perspective journal, June 1999

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Some analytic results concerning the mass spectrum of Yang-Mills gauge theories on a torus journal, June 1983

Relating ’t Hooft anomalies of 4d pure Yang-Mills and 2d ℂℙN− 1 model journal, October 2018

Quantum sine-Gordon equation as the massive Thirring model journal, April 1975

Fractional θ angle, ’t Hooft anomaly, and quantum instantons in charge-q multi-flavor Schwinger model journal, July 2019

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

Confinement from Center Vortices: A review of old and new results text, January 2016

Instanton-like contributions to the dynamics of Yang-Mills fields on the twisted torus journal, May 1993

A PCAC puzzle: π0→γγ in the σ-model journal, March 1969

Goldstone fields in two dimensions with multivalued actions journal, June 1984

Monopoles and instantons on partially compactified D -branes journal, September 1997

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

Coupling a QFT to a TQFT and duality journal, April 2014

Connection between center vortices and instantons through gauge-field smoothing journal, October 2015

Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory journal, September 1994

Some results for SU(N) gauge-fields on the Hypertorus journal, December 1982

Hidden Topological Angles in Path Integrals journal, July 2015

Solitons in the Higgs phase: the moduli matrix approach journal, June 2006

Exact T-duality between calorons and Taub-NUT spaces journal, June 1998

Confinement and deconfinement for any gauge group from dyons viewpoint conference, January 2011

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

θ -dependence and center symmetry in Yang-Mills theories journal, February 2020

A semiclassical realization of infrared renormalons text, January 2012

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

Constructing SU(N) fractional instantons journal, February 2020

New Nonperturbative Methods in Quantum Field Theory: From Large- N Orbifold Equivalence to Bions and Resurgence journal, October 2016

Instatons, the quark model, and the 1/N expansion journal, March 1979

Confinement of quarks journal, October 1974

A mechanism for quark confinement journal, February 1977

Twisted-Eguchi-Kawai model: A reduced model for large- N lattice gauge theory journal, May 1983

2d affine XY-spin model/4d gauge theory duality and deconfinement journal, April 2012

θ dependence of the deconfining phase transition in pure S U ( N c ) Yang-Mills theories journal, October 2013

Center vortex model for the infrared sector of SU(3) Yang-Mills theory: Topological susceptibility journal, January 2011

Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions journal, September 2009

Can We Make Sense Out of “Quantum Chromodynamics”? book, January 1979

Ordering, metastability and phase transitions in two-dimensional systems journal, April 1973

Circle compactification and ’t Hooft anomaly journal, December 2017

Minimum action solutions for SU(2) gauge theory on the torus with non-orthogonal twist journal, January 1990

Does the crossover from perturbative to nonperturbative physics in QCD become a phase transition at infinite N? journal, November 2003

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

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

The massive multi-flavor Schwinger model journal, May 1995

A property of electric and magnetic flux in non-Abelian gauge theories journal, January 1979

SU(2) calorons and magnetic monopoles journal, June 1998

Supersymmetric index in four-dimensional gauge theories journal, January 2001

Impossibility of spontaneously breaking local symmetries journal, December 1975

Exact resurgent trans-series and multibion contributions to all orders journal, May 2017

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

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Modified instanton sum in QCD and higher-groups journal, March 2020

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

Field Theories of Condensed Matter Physics
book, January 2013

The Confinement Problem in Lattice Gauge Theory
text, January 2003

θ dependence of SU(N) gauge theories in the presence of a topological term
journal, January 2009

Mass generation by fractional instantons in SU( n ) chains
journal, June 2020

QCD on a small circle
journal, November 2017

New higher anomalies, SU(N) Yang–Mills gauge theory and ${CP}^{N - 1}$ sigma model
journal, January 2020

Toward a theory of the strong interactions
journal, May 1978

Phase transitions and local minima of the action
journal, December 1982

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

Center-stabilized Yang-Mills theory: Confinement and large $N$ volume independence
journal, September 2008

Constraints on supersymmetry breaking
journal, July 1982

The critical properties of the two-dimensional xy model
journal, March 1974

Instantons in the Higgs phase
journal, July 2005

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

The topological objects near the chiral crossover transition in QCD
journal, July 2019

Light quarks in the screened dyon-antidyon Coulomb liquid model. II.
journal, October 2015

Confinement from Center Vortices: A review of old and new results
journal, January 2017

Confining dyon-antidyon Coulomb liquid model. I.
journal, October 2015

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

Semiclassical Realization of Infrared Renormalons
journal, September 2012

Calorons on the lattice - a new perspective
journal, June 1999

Quantum fluctuations of instantons in the nonlinear σ model
journal, July 1979

Some analytic results concerning the mass spectrum of Yang-Mills gauge theories on a torus
journal, June 1983

Relating ’t Hooft anomalies of 4d pure Yang-Mills and 2d ℂℙN− 1 model
journal, October 2018

Quantum sine-Gordon equation as the massive Thirring model
journal, April 1975

Fractional θ angle, ’t Hooft anomaly, and quantum instantons in charge-q multi-flavor Schwinger model
journal, July 2019

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

Confinement from Center Vortices: A review of old and new results
text, January 2016

Instanton-like contributions to the dynamics of Yang-Mills fields on the twisted torus
journal, May 1993

A PCAC puzzle: π0→γγ in the σ-model
journal, March 1969

Goldstone fields in two dimensions with multivalued actions
journal, June 1984

Monopoles and instantons on partially compactified $D$ -branes
journal, September 1997

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

Coupling a QFT to a TQFT and duality
journal, April 2014

Connection between center vortices and instantons through gauge-field smoothing
journal, October 2015

Electric-magnetic duality, monopole condensation, and confinement in N=2 supersymmetric Yang-Mills theory
journal, September 1994

Some results for SU(N) gauge-fields on the Hypertorus
journal, December 1982

Hidden Topological Angles in Path Integrals
journal, July 2015

Solitons in the Higgs phase: the moduli matrix approach
journal, June 2006

Exact T-duality between calorons and Taub-NUT spaces
journal, June 1998

Confinement and deconfinement for any gauge group from dyons viewpoint
conference, January 2011

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

θ -dependence and center symmetry in Yang-Mills theories
journal, February 2020

A semiclassical realization of infrared renormalons
text, January 2012

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

Constructing SU(N) fractional instantons
journal, February 2020

New Nonperturbative Methods in Quantum Field Theory: From Large- N Orbifold Equivalence to Bions and Resurgence
journal, October 2016

Instatons, the quark model, and the 1/N expansion
journal, March 1979

Confinement of quarks
journal, October 1974

A mechanism for quark confinement
journal, February 1977

Twisted-Eguchi-Kawai model: A reduced model for large- $N$ lattice gauge theory
journal, May 1983

2d affine XY-spin model/4d gauge theory duality and deconfinement
journal, April 2012

$θ$ dependence of the deconfining phase transition in pure $S U (N_{c})$ Yang-Mills theories
journal, October 2013

Center vortex model for the infrared sector of SU(3) Yang-Mills theory: Topological susceptibility
journal, January 2011

Magnetic bion condensation: A new mechanism of confinement and mass gap in four dimensions
journal, September 2009

Can We Make Sense Out of “Quantum Chromodynamics”?
book, January 1979

Ordering, metastability and phase transitions in two-dimensional systems
journal, April 1973

Circle compactification and ’t Hooft anomaly
journal, December 2017

Minimum action solutions for SU(2) gauge theory on the torus with non-orthogonal twist
journal, January 1990

Does the crossover from perturbative to nonperturbative physics in QCD become a phase transition at infinite N?
journal, November 2003

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

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

The massive multi-flavor Schwinger model
journal, May 1995

A property of electric and magnetic flux in non-Abelian gauge theories
journal, January 1979

SU(2) calorons and magnetic monopoles
journal, June 1998

Supersymmetric index in four-dimensional gauge theories
journal, January 2001

Impossibility of spontaneously breaking local symmetries
journal, December 1975

Exact resurgent trans-series and multibion contributions to all orders
journal, May 2017

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

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

Order Parameters and Color-Flavor Center Symmetry in QCD
journal, November 2017

Modified instanton sum in QCD and higher-groups
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Confining ensemble of dyons
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Instanton Constituents in the O(3) Model at Finite Temperature
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Numerical analysis of fractional charge solutions on the torus
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Bosonized massive N -flavour Schwinger model
journal, December 1998

Abelian Duality, Confinement, and Chiral-Symmetry Breaking in a SU(2) QCD-Like Theory
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Gauge invariant structures and confinement
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Infrared renormalon in the supersymmetric $\mathbb{C}P^{N-1}$ model on $\mathbb{R}\times S^1$
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Theta, time reversal and temperature
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