Abstract
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.
Highlights
The Landau background gauge, known as the Landau–DeWitt gauge, has found renewed interest during the past decade given its usefulness in accessing the confinementdeconfinement transition via the vacuum expectation value of the Polyakov loop, describable via an appropriate background
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
Motivated by the observation in [13] that in the background field formalism, BRST invariance at the quantum level is closely linked to background gauge invariance at the classical level, in Section 3 we go on remedying this problem by constructing a BRST and background invariant version of the Gribov–Zwanziger action, the latter still capable of mitigating the Gribov copy problem but no longer exhibiting the undesirable unphysical features at zero temperature
Summary
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. Succeeding in the latter, we identify a major drawback, shared with the conjectured action in [21, 22]: even at zero temperature, a nonzero value of a Lorentz symmetry breaking background is energetically favoured. Motivated by the observation in [13] that in the background field formalism, BRST invariance at the quantum level is closely linked to background gauge invariance at the classical level, in Section 3 we go on remedying this problem by constructing a BRST and background invariant version of the Gribov–Zwanziger action, the latter still capable of mitigating the Gribov copy problem but no longer exhibiting the undesirable unphysical features at zero temperature
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