### Abstract

The Yang-Mills gradient flow and its extension to the fermion field provide a very general method to obtain renormalized observables in gauge theory. The method is applicable also with non- perturbative regularization such as lattice. The gradient flow thus offers useful probes to study non-perturbative dynamics of gauge theory. In this work, aiming at possible simplification in per-Turbative calculations associated with the gradient flow, a modification of the gauge-fixed version of the flow equation, which preserves gauge covariance under the background gauge transforma-Tion, is proposed. This formulation allows for example a very quick one-loop calculation of the small flow time expansion of a composite operator that is relevant to the construction of a lattice energy-momentum tensor. Some details of the calculation, which have not been given elsewhere, are presented.

Original language | English |
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Article number | 304 |

Journal | Proceedings of Science |

Volume | 14-18-July-2015 |

Publication status | Published - Jan 1 2015 |

Event | 33rd International Symposium on Lattice Field Theory, LATTICE 2015 - Kobe, Japan Duration: Jul 14 2015 → Jul 18 2015 |

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### All Science Journal Classification (ASJC) codes

- General

### Cite this

*Proceedings of Science*,

*14-18-July-2015*, [304].

**Background field method in the gradient flow.** / Suzuki, Hiroshi.

Research output: Contribution to journal › Conference article

*Proceedings of Science*, vol. 14-18-July-2015, 304.

}

TY - JOUR

T1 - Background field method in the gradient flow

AU - Suzuki, Hiroshi

PY - 2015/1/1

Y1 - 2015/1/1

N2 - The Yang-Mills gradient flow and its extension to the fermion field provide a very general method to obtain renormalized observables in gauge theory. The method is applicable also with non- perturbative regularization such as lattice. The gradient flow thus offers useful probes to study non-perturbative dynamics of gauge theory. In this work, aiming at possible simplification in per-Turbative calculations associated with the gradient flow, a modification of the gauge-fixed version of the flow equation, which preserves gauge covariance under the background gauge transforma-Tion, is proposed. This formulation allows for example a very quick one-loop calculation of the small flow time expansion of a composite operator that is relevant to the construction of a lattice energy-momentum tensor. Some details of the calculation, which have not been given elsewhere, are presented.

AB - The Yang-Mills gradient flow and its extension to the fermion field provide a very general method to obtain renormalized observables in gauge theory. The method is applicable also with non- perturbative regularization such as lattice. The gradient flow thus offers useful probes to study non-perturbative dynamics of gauge theory. In this work, aiming at possible simplification in per-Turbative calculations associated with the gradient flow, a modification of the gauge-fixed version of the flow equation, which preserves gauge covariance under the background gauge transforma-Tion, is proposed. This formulation allows for example a very quick one-loop calculation of the small flow time expansion of a composite operator that is relevant to the construction of a lattice energy-momentum tensor. Some details of the calculation, which have not been given elsewhere, are presented.

UR - http://www.scopus.com/inward/record.url?scp=84988564380&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84988564380&partnerID=8YFLogxK

M3 - Conference article

AN - SCOPUS:84988564380

VL - 14-18-July-2015

JO - Proceedings of Science

JF - Proceedings of Science

SN - 1824-8039

M1 - 304

ER -