### Abstract

We propose a 5-dimensional definition for the physical 4D-Yang-Mills theory. The fifth dimension corresponds to the Monte Carlo time of numerical simulations of QCD_{4}. The 5-dimensional theory is a well-defined topological quantum field theory that can be renormalized at any given finite order of perturbation theory. The relation to nonperturbative physics is obtained by expressing the theory on a lattice, a la Wilson. The new fields that must be introduced in the context of a topological Yang-Mills theory have a simple lattice expression. We present a 5-dimensional critical limit for physical correlation functions and for dynamical autocorrelations, which allows new Monte Carlo algorithm based on the time-step in lattice units given by ε=g_{0}
^{-13/11} in pure gluodynamics. The gauge-fixing in five dimensions is such that no Gribov ambiguity occurs. The weight is strictly positive, because all ghost fields have parabolic propagators and yield trivial determinants. We indicate how our 5-dimensional description of the Yang-Mills theory may be extended to fermions.

Original language | English (US) |
---|---|

Pages (from-to) | 604-640 |

Number of pages | 37 |

Journal | Nuclear Physics, Section B |

Volume | 581 |

Issue number | 1-2 |

State | Published - Aug 14 2000 |

### Fingerprint

### Keywords

- 11.10.Kk
- 11.15.-q
- 12.28.Aw

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

### Cite this

*Nuclear Physics, Section B*,

*581*(1-2), 604-640.

**QCD 4 from a five-dimensional point of view.** / Baulieu, Laurent; Zwanziger, Daniel.

Research output: Contribution to journal › Article

*Nuclear Physics, Section B*, vol. 581, no. 1-2, pp. 604-640.

}

TY - JOUR

T1 - QCD 4 from a five-dimensional point of view

AU - Baulieu, Laurent

AU - Zwanziger, Daniel

PY - 2000/8/14

Y1 - 2000/8/14

N2 - We propose a 5-dimensional definition for the physical 4D-Yang-Mills theory. The fifth dimension corresponds to the Monte Carlo time of numerical simulations of QCD4. The 5-dimensional theory is a well-defined topological quantum field theory that can be renormalized at any given finite order of perturbation theory. The relation to nonperturbative physics is obtained by expressing the theory on a lattice, a la Wilson. The new fields that must be introduced in the context of a topological Yang-Mills theory have a simple lattice expression. We present a 5-dimensional critical limit for physical correlation functions and for dynamical autocorrelations, which allows new Monte Carlo algorithm based on the time-step in lattice units given by ε=g0 -13/11 in pure gluodynamics. The gauge-fixing in five dimensions is such that no Gribov ambiguity occurs. The weight is strictly positive, because all ghost fields have parabolic propagators and yield trivial determinants. We indicate how our 5-dimensional description of the Yang-Mills theory may be extended to fermions.

AB - We propose a 5-dimensional definition for the physical 4D-Yang-Mills theory. The fifth dimension corresponds to the Monte Carlo time of numerical simulations of QCD4. The 5-dimensional theory is a well-defined topological quantum field theory that can be renormalized at any given finite order of perturbation theory. The relation to nonperturbative physics is obtained by expressing the theory on a lattice, a la Wilson. The new fields that must be introduced in the context of a topological Yang-Mills theory have a simple lattice expression. We present a 5-dimensional critical limit for physical correlation functions and for dynamical autocorrelations, which allows new Monte Carlo algorithm based on the time-step in lattice units given by ε=g0 -13/11 in pure gluodynamics. The gauge-fixing in five dimensions is such that no Gribov ambiguity occurs. The weight is strictly positive, because all ghost fields have parabolic propagators and yield trivial determinants. We indicate how our 5-dimensional description of the Yang-Mills theory may be extended to fermions.

KW - 11.10.Kk

KW - 11.15.-q

KW - 12.28.Aw

UR - http://www.scopus.com/inward/record.url?scp=0000402602&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000402602&partnerID=8YFLogxK

M3 - Article

VL - 581

SP - 604

EP - 640

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

IS - 1-2

ER -