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On Gauge Consistency In Gauge-Fixed Yang-Mills Theory
by Jan M. Pawlowski, Coralie S. Schneider, Nicolas Wink
Submission summary
| Authors (as registered SciPost users): | Jan M. Pawlowski · Nicolas Wink |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2202.11123v2 (pdf) |
| Date submitted: | Aug. 26, 2022, 9:45 a.m. |
| Submitted by: | Nicolas Wink |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
We investigate BRST invariance in Landau gauge Yang-Mills theory with functional methods. To that end, we solve the coupled system of functional renormalisation group equations for the momentum-dependent ghost and gluon propagator, ghost-gluon, and three- and four-gluon vertex dressings. The equations for both, transverse and longitudinal correlation functions are solved self-consistently: all correlation functions are fed back into the loops. Additionally, we also use the Slavnov-Taylor identities for computing the longitudinal correlation functions on the basis of the above results. Then, the gauge consistency of the solutions is checked by comparing the respective longitudinal correlation functions. We find good agreement of these results, hinting at the gauge consistency of our setup.
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1. Why are the initial values of the ghost-gluon coupling and the three-, four-gluon couplings chosen differently? In this deep ultraviolet (UV) region, the FRG flows even with the truncations in this work should be consistent with the perturbative flows. It is difficult to see the reason why different vertex dressings at the UV cutoff are required to tune the dressings at large momenta at k=0.
2. What is the relation between the emergence of gluon mass gap and the breaking of BRST symmetry in the infrared region as shown in Fig.8, Fig.11? Is the breaking of BRST is a necessary condition for the emergence of gluon mass gap?
3. Usually the BRST symmetry plays a key role in guaranteeing the renormalizability of the theory. The BRST symmetry is lost when the regulators are implemented. So, how does the renormalizability is warranted after the BRST symmetry is broken?
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Jennifer Nielsen on 2025-06-03 [id 5538]
Highlights/strengths: The paper presents a unique contribution to gauge theory via an original solution for both the functional renormalization group (FRG) equations and modified Slavnov-Taylor identities (mSTIs) which is self-consistent for longitudinal and transverse Yang-Mills correlation functions. The paper further highlights a non-trivial subtlety--that only RG-adapted regulators yield self-consistent mass terms between fRG and mSTI frameworks. This is both technically original and conceptually important for preserving BRST structure in truncated systems. The authors make a strong case for using deviations in longitudinal correlators as diagnostics for gauge (in)consistency. By tuning initial conditions, the authors demonstrate continuity between decoupling, scaling, and Higgs-type solutions, providing a useful reference map for connecting various pictures of confinement. Rather than using STIs as fixed constraints, the authors use STI violation to evaluate the health of truncations, which is pragmatic and well-grounded and justified by the literature despite novelty.
The structure of the paper clean and clear with detailed derivations and relevant appendices. The authors are transparent about the scope and limitations of their project.
Questions:
How sensitive are your results to the choice of regulator beyond RG-adapted classes?
Could non-adapted regulators lead to spurious mass terms? Which observables are most affected?
Can your approach generalize to gauges other than Landau? Does your framework have a route to Feynman gauge or Coulomb gauge formulations?
Have you explored the impact of including non-classical tensor structures in the vertices, considering that some STIs depend on assumptions of regularity that may not hold in the deep IR?
How stable is the gauge consistency when quarks are included (i.e., moving toward full QCD)?
Would including matter fields disrupt the closure of the transverse sector, or introduce STI violations?
Can the deviation of mSTIs at small momenta be quantitatively connected to confinement diagnostics?
This could provide insights with respect to using BRST (in)consistency as confinement criteria.
Concerns: Reliance on a truncation of the infinite hierarchy of functional equations (vertex expansion up to 4-point functions) is a sophisticated approach, but there is potential omission of non-classical tensor structures and higher-loop effects that might effect BRST consistency in deep IR. This implies mSTIs may not be satisfied in the IR due to truncation artifacts. In some STIs (especially those involving the longitudinal 3- and 4-gluon vertices), the paper assumes regularity of certain projections. This might suppress physical irregularities essential for dynamically generated mass gaps or non-perturbative BRST breaking/restoration. Despite attempt to use RG-adapted regulators, there remains an inherent regulator-dependence in the mSTI results, especially at small 𝑘. There could be implicit mass-like terms introduced by the choice of regulator, which may in turn impact the interpretation of dynamical gluon mass. Figure 8 and Figure 9 show small but non-vanishing violations of the mSTIs , especially in decoupling and Higgs-type branches. These deviations are discussed in relation to truncation, but raise flags regarding gauge consistency across the full momentum range. There could be issues associated with the assumption of equal initial conditions: the longitudinal and transverse dressings are initialized identically in their numerical procedure, which may bias the solution toward BRST-like behavior.