背景不变性下的朗道-德威特规范复制：限制与解除约束的新洞察

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本文探讨的是在量子场论特别是规范场论中，一个关键的主题——朗道-德威特（Landau-DeWitt）量规下的量规副本（gauge copies）。朗道背景测量仪，以其与Polyakov环的关联而受到广泛关注，Polyakov环的真空期望值在研究 confinement-deconfinement相变时起着重要作用。背景不变性是这个分析的核心，因为通过背景描述可以揭示物理现象的内在结构。在过去的十年里，Landau-DeWitt gauge因其在处理规范理论中背景独立性的独特优势，重新引起了研究者的兴趣。Gribov-Zwanziger理论是这种背景下的一种重要进展，它采用了一种背景不变的方式来概括规范变换下的有效行动。作者David Dudala和David Vercauteren从Gribov副本的角度来审视这个量规，这是一种特殊的规范变换，它可能导致额外的物理解，这些解在经典规范理论中并不显著，但在量子层面上却可能有重要影响。他们回顾了Gribov副本的概念，并将其与Landau-DeWitt gauge的规范不变性相结合。在BRST（Becchi-Rouet-Stora-Tyutin）框架下，他们对Gribov-Zwanziger的有效行动进行了概括，这个行动是通过消除Gribov副本带来的冗余度来实现的。BRST方法是一种重要的工具，用于处理量子场论中的冗余度问题，确保物理结果的背景独立性。文章的主要贡献在于提供了一个全新的视角来理解Landau-DeWitt gauge中的规范复制，并展示了如何通过背景不变性限制来处理这些复制。这不仅有助于深化我们对规范场论基础的理解，而且可能对探索QCD（量子 chromodynamics，量子色动力学）中的confinement现象以及高能物理中的其他相关问题有所启发。文章于2018年2月接收并修改后被接受，同年2月在线发布，编辑为M.Cvetič。对于物理学家、理论物理爱好者以及那些研究量子场论和规范理论的研究生而言，这篇工作提供了一个深入研究规范不变性限制及其在量子规范系统中的实际应用的重要资源。

Physics Letters B 779 (2018) 275–282

Contents lists available at ScienceDirect

Physics Letters B

www.elsevier.com/locate/physletb

Gauge copies in the Landau–DeWitt gauge: A background invariant

restriction

David Dudal

a,b,∗

, David Vercauteren

KU Leuven Campus Kortrijk – Kulak, Department of Physics, Etienne Sabbelaan 53 bus 7657, 8500 Kortrijk, Belgium

Ghent University, Department of Physics and Astronomy, Krijgslaan 281-S9, 9000 Gent, Belgium

Duy Tân University, Institute of Research and Development, P809, 3 Quang Trung, Hải Châu, Ðà Nẵng, Viet Nam

a r t i c l e i n f o a b s t r a c t

Article history:

Received

1 December 2017

Received

in revised form 5 February 2018

Accepted

9 February 2018

Available

online 13 February 2018

Editor:

M. Cveti

The Landau background gauge, also known as the Landau–DeWitt gauge, has found renewed interest

during the past decade given its usefulness in accessing the conﬁnement-deconﬁnement transition via

the vacuum expectation value of the Polyakov loop, describable via an appropriate background. In this

Letter, we revisit this gauge from the viewpoint of it displaying gauge (Gribov) copies. We generalize

the Gribov–Zwanziger effective action in a BRST and background invariant way; this action leads to a

restriction on the allowed gauge ﬂuctuations, thereby eliminating the inﬁnitesimal background gauge

copies. The explicit background invariance of our action is in contrast with earlier attempts to write

down and use an effective Gribov–Zwanziger action. It allows to address certain subtleties arising in

these earlier works, such as a spontaneous and thus spurious Lorentz symmetry breaking, something

which is now averted.

(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP

1. Introduction

A powerful quantization procedure for locally gauge invariant

Yang–Mills theories is the background ﬁeld formalism, in which

formalism the gauge ﬁeld is split in a non-propagating “classical”

background and a ﬂuctuating quantum part which is integrated

over in the path integral procedure. Just as when dealing with an

ordinary gauge theory, the quantum gauge ﬁelds need to be gauge

ﬁxed in the continuum. A particularly useful class of gauges in this

context are the background covariant gauges; in these gauges, the

background ﬁeld formalism possesses the important property that,

after gauge ﬁxing of and integration over the quantum ﬁelds, the

eventual (effective) action ought to still be invariant with respect

to gauge transformations of the background ﬁelds. Useful refer-

ences

are [1,2].

Background

gauges found a renewed interest during the past

decade thanks to their usefulness in probing a typical (non-local)

order parameter for the deconﬁnement transition, the Polyakov

loop, whose behaviour can be encoded in a simple speciﬁc back-

ground,

see [3–9]. Also in the pinch technique combined with

Dyson–Schwinger equations, the background ﬁeld formalism plays

Corresponding author.

E-mail

addresses: david .dudal @kuleuven .be (D. Dudal),

vercauterendavid @dtu .edu .vn (D. Vercauteren).

a central role [10–12]. Algebraic aspects of a speciﬁc background

gauge, the Landau–DeWitt one, including an all order renormaliz-

ability

proof, were considered in [13–15].

Albeit

powerful, the (covariant) background gauges are also not

free from the famous Gribov ambiguity [16] hampering the quanti-

zation:

multiple gauge equivalent copies of a given quantum gauge

ﬁeld obey the same gauge condition. To deal with this ambiguity,

one possibility is to further constrain the space of gauge conﬁgu-

rations

to be integrated over in the path integral, a procedure pro-

posed

by Gribov in [16]and worked out by Zwanziger in e.g. [17,

18]for

the standard Landau gauge. The end point is an effective

action — the Gribov–Zwanziger action — implementing this restric-

tion.

More references can be found in [19].

the presence of backgrounds, seminal work is [20], based

on which a background version of the Gribov–Zwanziger effec-

tive

action was proposed and used to probe non-perturbative ﬁnite

temperature dynamics in [21,22].

this Letter, we revisit in Section 2 the problem of Gribov

copies in the Landau–DeWitt gauge and try to derive a Gribov–

Zwanziger

action. Although succeeding in the latter, we identify

a major drawback, shared with the conjectured action in [21,22]:

even at zero temperature, a non-zero value of a Lorentz symme-

try

breaking background is energetically favoured. The problem is

traced back to the lack of background gauge invariance and, un-

derlyingly,

of BRST invariance of the original Gribov–Zwanziger

approach. Motivated by the observation in [13] that in the back-

https://doi.org/10.1016/j.physletb.2018.02.014

0370-2693/

SCOAP

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