Loop equations and bootstrap methods in the lattice

Anderson, Peter D.; Kruczenski, Martin

doi:10.1016/j.nuclphysb.2017.06.009

Title: Loop equations and bootstrap methods in the lattice

Abstract

Pure gauge theories can be formulated in terms of Wilson Loops by means of the loop equation. In the large-N limit this equation closes in the expectation value of single loops. In particular, using the lattice as a regulator, it becomes a well defined equation for a discrete set of loops. In this paper we study different numerical approaches to solving this equation.

Authors:: Anderson, Peter D.; Kruczenski, Martin

Publication Date:: Tue Aug 01 00:00:00 EDT 2017

Research Org.:: Purdue Univ., West Lafayette, IN (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1365593

Alternate Identifier(s):: OSTI ID: 1425890

Grant/Contract Number:: SC0007884; SC0007901

Resource Type:: Published Article

Journal Name:: Nuclear Physics. B

Additional Journal Information:: Journal Name: Nuclear Physics. B Journal Volume: 921 Journal Issue: C; Journal ID: ISSN 0550-3213

Publisher:: Elsevier

Country of Publication:: Netherlands

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats


                    Anderson, Peter D., and Kruczenski, Martin. Loop equations and bootstrap methods in the lattice.  Netherlands: N. p., 2017. 
Web.  doi:10.1016/j.nuclphysb.2017.06.009.

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                    Anderson, Peter D., & Kruczenski, Martin. Loop equations and bootstrap methods in the lattice.  Netherlands.  https://doi.org/10.1016/j.nuclphysb.2017.06.009

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                    Anderson, Peter D., and Kruczenski, Martin. Tue .  
"Loop equations and bootstrap methods in the lattice".  Netherlands.  https://doi.org/10.1016/j.nuclphysb.2017.06.009.

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@article{osti_1365593,

  title        = {Loop equations and bootstrap methods in the lattice},

  author       = {Anderson, Peter D. and Kruczenski, Martin},

  abstractNote = {Pure gauge theories can be formulated in terms of Wilson Loops by means of the loop equation. In the large-N limit this equation closes in the expectation value of single loops. In particular, using the lattice as a regulator, it becomes a well defined equation for a discrete set of loops. In this paper we study different numerical approaches to solving this equation.},

  doi          = {10.1016/j.nuclphysb.2017.06.009},

  journal      = {Nuclear Physics. B},

  number       = C,

  volume       = 921,

  place        = {Netherlands},

  year         = {Tue Aug 01 00:00:00 EDT 2017},

  month        = {Tue Aug 01 00:00:00 EDT 2017}

}

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Title: Loop equations and bootstrap methods in the lattice

Abstract

Citation Formats

Universal constraints on conformal operator dimensions journal, August 2009

The large-N phase transition of lattice SU(N) gauge theories journal, March 1999

String theory and quark confinement journal, November 1998

Large N limits as classical mechanics journal, April 1982

Exact equation for the loop average in multicolor QCD journal, December 1979

Gauge theory correlators from non-critical string theory journal, May 1998

Strong-coupling expansion for lattice Yang-Mills fields journal, October 1978

A gauge-invariant Hamiltonian analysis for non-Abelian gauge theoreiesin (2+1) dimensions journal, April 1996

The large $N$ limit of superconformal field theories and supergravity journal, January 1998

Anti de Sitter space and holography journal, January 1998

Exact lattice supersymmetry journal, November 2009

Possible third-order phase transition in the large- N lattice gauge theory journal, January 1980

Field theory of strings as a collective field theory of U ( N ) gauge fields journal, February 1980

Loop space Hamiltonians and numerical methods for large-N gauge theories journal, March 1983

On the vacuum wavefunction and string tension of Yang-Mills theories in (2+1) dimensions journal, August 1998

An object oriented code for simulating supersymmetric Yang–Mills theories journal, June 2012

Loop dynamics for gauge theories: A numerical algorithm journal, June 1984

Loop dynamics and AdS/CFT correspondence journal, January 2001

Implementation and evaluation of SDPA 6.0 (Semidefinite Programming Algorithm 6.0) journal, August 2003

Loop equations and 1N expansion journal, December 1983

Strong coupling and mean field methods in lattice gauge theories journal, December 1983

Multicolor QCD in terms of random surfaces journal, April 1984

Gauge fields–strings duality and the loop equation journal, August 2000

Yang—Mills theory - a string theory in disguise journal, October 1979

On the random-surface representation of U(∞) lattice gauge theory journal, November 1984

Planar Yang-Mills theory: Hamiltonian, regulators and mass gap journal, August 1998

Lattice gauge models in the strong-coupling regime journal, May 1977

The quantum collective field method and its application to the planar limit journal, April 1980

Parallel software for lattice N = 4 supersymmetric Yang–Mills theory journal, May 2015

Gauge fields as rings of glue journal, January 1980

Loop-space hamiltonians and numerical methods for large-N gauge theories (II) journal, March 1984

Phase transition in SU(6) lattice gauge theory journal, March 1982

Convergence of the iterative solution of loop equations in planar QCD2 journal, January 1985

Collective field approach to the large-N limit: Euclidean field theories journal, July 1981

Solving Pure Yang-Mills Theory in 2 + 1 Dimensions journal, June 2006

Manifest covariance and the Hamiltonian approach to mass gap in (2+1)-dimensional Yang-Mills theory journal, June 2001

Confinement of quarks journal, October 1974

One-loop perturbative calculation of Wilson loops on finite lattices journal, January 1985

The other topological twisting of N = 4 Yang-Mills journal, October 1995

On the origin of the mass gap for non-Abelian gauge theories in (2+1) dimensions journal, June 1996

A two-dimensional model for mesons journal, June 1974

N = 4 supersymmetry on a space-time lattice journal, September 2014

Loop-space representation and the large- N behavior of the one-plaquette Kogut-Susskind Hamiltonian journal, July 1980

U(∞) lattice gauge theory as a free lattice string theory journal, September 1983

A planar diagram theory for strong interactions journal, April 1974

Dyson-Schwinger equations approach to the large- N limit: Model systems and string representation of Yang-Mills theory journal, August 1981

Properties of the loop average in QCD journal, May 1980

The spectrum of Yang–Mills theory in 2+1 dimensions, analytically journal, June 2007

Semidefinite Programming journal, March 1996

Self-consistent area law in QCD journal, December 1980

Strings in U(N) lattice gauge theory journal, October 1979

Some nonabelian toy models in the largeN limit journal, January 1981

Universal constraints on conformal operator dimensions
journal, August 2009

The large-N phase transition of lattice SU(N) gauge theories
journal, March 1999

String theory and quark confinement
journal, November 1998

Large $N$ limits as classical mechanics
journal, April 1982

Exact equation for the loop average in multicolor QCD
journal, December 1979

Gauge theory correlators from non-critical string theory
journal, May 1998

Strong-coupling expansion for lattice Yang-Mills fields
journal, October 1978

A gauge-invariant Hamiltonian analysis for non-Abelian gauge theoreiesin (2+1) dimensions
journal, April 1996

The large $N$ limit of superconformal field theories and supergravity
journal, January 1998

Anti de Sitter space and holography
journal, January 1998

Exact lattice supersymmetry
journal, November 2009

Possible third-order phase transition in the large- $N$ lattice gauge theory
journal, January 1980

Field theory of strings as a collective field theory of $U (N)$ gauge fields
journal, February 1980

Loop space Hamiltonians and numerical methods for large-N gauge theories
journal, March 1983

On the vacuum wavefunction and string tension of Yang-Mills theories in (2+1) dimensions
journal, August 1998

An object oriented code for simulating supersymmetric Yang–Mills theories
journal, June 2012

Loop dynamics for gauge theories: A numerical algorithm
journal, June 1984

Loop dynamics and AdS/CFT correspondence
journal, January 2001

Implementation and evaluation of SDPA 6.0 (Semidefinite Programming Algorithm 6.0)
journal, August 2003

Loop equations and 1N expansion
journal, December 1983

Strong coupling and mean field methods in lattice gauge theories
journal, December 1983

Multicolor QCD in terms of random surfaces
journal, April 1984

Gauge fields–strings duality and the loop equation
journal, August 2000

Yang—Mills theory - a string theory in disguise
journal, October 1979

On the random-surface representation of U(∞) lattice gauge theory
journal, November 1984

Planar Yang-Mills theory: Hamiltonian, regulators and mass gap
journal, August 1998

Lattice gauge models in the strong-coupling regime
journal, May 1977

The quantum collective field method and its application to the planar limit
journal, April 1980

Parallel software for lattice $N = 4$ supersymmetric Yang–Mills theory
journal, May 2015

Gauge fields as rings of glue
journal, January 1980

Loop-space hamiltonians and numerical methods for large-N gauge theories (II)
journal, March 1984

Phase transition in SU(6) lattice gauge theory
journal, March 1982

Convergence of the iterative solution of loop equations in planar QCD2
journal, January 1985

Collective field approach to the large-N limit: Euclidean field theories
journal, July 1981

Solving Pure Yang-Mills Theory in $2 + 1$ Dimensions
journal, June 2006

Manifest covariance and the Hamiltonian approach to mass gap in (2+1)-dimensional Yang-Mills theory
journal, June 2001

Confinement of quarks
journal, October 1974

One-loop perturbative calculation of Wilson loops on finite lattices
journal, January 1985

The other topological twisting of N = 4 Yang-Mills
journal, October 1995

On the origin of the mass gap for non-Abelian gauge theories in (2+1) dimensions
journal, June 1996

A two-dimensional model for mesons
journal, June 1974

$N = 4$ supersymmetry on a space-time lattice
journal, September 2014

Loop-space representation and the large- $N$ behavior of the one-plaquette Kogut-Susskind Hamiltonian
journal, July 1980

U(∞) lattice gauge theory as a free lattice string theory
journal, September 1983

A planar diagram theory for strong interactions
journal, April 1974

Dyson-Schwinger equations approach to the large- $N$ limit: Model systems and string representation of Yang-Mills theory
journal, August 1981

Properties of the loop average in QCD
journal, May 1980

The spectrum of Yang–Mills theory in 2+1 dimensions, analytically
journal, June 2007

Semidefinite Programming
journal, March 1996

Self-consistent area law in QCD
journal, December 1980

Strings in U(N) lattice gauge theory
journal, October 1979

Some nonabelian toy models in the largeN limit
journal, January 1981