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arxiv: 2511.09752 · v1 · submitted 2025-11-12 · ✦ hep-th

On BRST-Related Symmetries in the FLPR Model with Gribov Ambiguities

Bhabani Prasad Mandal , Sumit Kumar Rai , Ronaldo Thibes This is my paper

Pith reviewed 2026-05-17 21:53 UTC · model grok-4.3

classification ✦ hep-th
keywords BRST symmetriesGribov ambiguitiesFLPR modelgauge fixingQCDfunctional quantizationdiscrete symmetriessymmetry violation
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The pith

Gauges with Gribov ambiguities violate the discrete group of symmetries of the gauge-fixed action in the FLPR model.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper investigates the FLPR model using a framework of BRST-related symmetries and carries out its full functional quantization as a gauge-invariant system while accounting for Gribov ambiguities. It derives a family of BRST-related transformations generated by the discrete group of symmetries of the action. The central result is that gauges possessing Gribov ambiguities cause a violation of those initial discrete symmetries in the gauge-fixed action. This setup establishes a correspondence between variables and fields in the FLPR model and QCD to illuminate similar symmetry issues in the latter.

Core claim

When gauges that possess Gribov ambiguities are used in the FLPR model, the initial discrete group of symmetries of the gauge-fixed action is violated. This violation is uncovered by performing the complete functional quantization of the model in a BRST-related symmetries framework, yielding a family of BRST-related transformations that reflect the broken discrete symmetry group.

What carries the argument

The discrete group of symmetries of the gauge-fixed action, which generates BRST-related transformations but is violated when Gribov ambiguities are present in the chosen gauge.

If this is right

  • The symmetry violation supplies a concrete mechanism by which Gribov copies affect the quantized theory.
  • The family of BRST-related transformations remains available even after the discrete symmetry breaking.
  • The field and variable mapping between the FLPR model and QCD allows direct transfer of the symmetry-violation result to non-Abelian gauge theories.
  • Gauge choices without Gribov ambiguities are required to retain the original discrete symmetry group after quantization.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same symmetry-violation pattern may appear in other simplified models used to study the Gribov problem, offering a way to classify which gauges preserve or break discrete symmetries.
  • Adjustments to standard BRST quantization procedures could be needed whenever Gribov ambiguities are present, to restore a consistent symmetry structure.
  • The correspondence established here could be used to test whether certain non-perturbative effects in QCD are direct consequences of this discrete symmetry breaking.

Load-bearing premise

The FLPR model with its BRST framework accurately captures the essential Gribov-related symmetry issues present in QCD.

What would settle it

An explicit computation in one of the Gribov-ambiguous gauges of the FLPR model that preserves the full initial discrete symmetry group of the gauge-fixed action would falsify the central claim.

read the original abstract

With a recent revival, novel features of the FLPR model have been reported in the literature. A connection between those features to QCD involving the Gribov problem is explored. We investigate the FLPR model in a recently proposed framework of BRST-related symmetries and perform its full functional quantization as a gauge invariant system taking into account the Gribov ambiguities. We obtain a family of BRST-related transformations generated by the discrete group of symmetries of the action. We show that gauges possessing Gribov ambiguities lead to a violation of the initial discrete group of symmetries of the gauge-fixed action. The obtained results shed light into similar issues in QCD by the corresponding association of variables and fields between the two systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper examines the FLPR model within a BRST-related symmetries framework. It carries out the full functional quantization of the model as a gauge-invariant system while incorporating Gribov ambiguities. From the discrete symmetries of the gauge-fixed action, the authors derive a family of BRST-related transformations and demonstrate that these symmetries are violated in gauges that possess Gribov ambiguities. The results are then linked to analogous issues in QCD through an association of variables and fields between the two systems.

Significance. If the FLPR derivation is rigorous and the variable association preserves the action of the discrete symmetries, the work could illuminate how Gribov copies affect discrete symmetries in gauge-fixed actions, offering a simplified arena in which to study features relevant to QCD. The explicit construction of the BRST-related transformations from the discrete group and the functional quantization that includes the Gribov region constitute concrete technical contributions.

major comments (2)
  1. [Discussion of QCD implications (near end of manuscript)] The central extension to QCD rests on the statement that the FLPR results 'shed light into similar issues in QCD by the corresponding association of variables and fields.' No explicit mapping is supplied that verifies the discrete symmetry generators or their action on the gauge-fixed Lagrangian correspond under this association to the non-Abelian gauge fields, ghost sector, and horizon condition of QCD. Because this association is load-bearing for the broader claim, its justification must be supplied (e.g., by exhibiting the dictionary and checking invariance of the relevant operators).
  2. [Functional quantization section] The functional quantization step that incorporates Gribov ambiguities and produces the symmetry violation is presented as following directly from the BRST framework, yet the manuscript does not display the explicit form of the modified measure or the horizon condition used. Without these intermediate expressions it is impossible to confirm that the reported violation is a direct consequence rather than an artifact of an unstated truncation.
minor comments (2)
  1. [Section introducing BRST-related transformations] Notation for the discrete group generators and the associated BRST charges should be introduced with a clear table or list of commutation relations to aid readability.
  2. [Concluding remarks] A brief comparison table contrasting the FLPR discrete symmetries with the corresponding structures in standard Yang-Mills theory would help the reader assess the strength of the proposed association.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript on the FLPR model and its BRST-related symmetries in the presence of Gribov ambiguities. We address each major comment below and will revise the manuscript accordingly to improve clarity and strengthen the QCD connection.

read point-by-point responses

  1. Referee: [Discussion of QCD implications (near end of manuscript)] The central extension to QCD rests on the statement that the FLPR results 'shed light into similar issues in QCD by the corresponding association of variables and fields.' No explicit mapping is supplied that verifies the discrete symmetry generators or their action on the gauge-fixed Lagrangian correspond under this association to the non-Abelian gauge fields, ghost sector, and horizon condition of QCD. Because this association is load-bearing for the broader claim, its justification must be supplied (e.g., by exhibiting the dictionary and checking invariance of the relevant operators).

    Authors: We agree that the association between the FLPR model and QCD is central to the broader implications and that an explicit mapping would strengthen the presentation. The manuscript relies on a standard correspondence of variables and fields between the two systems, but we acknowledge that verifying the discrete symmetry generators and their action on the gauge-fixed Lagrangian (including the non-Abelian gauge fields, ghost sector, and horizon condition) requires a more detailed dictionary. In the revised version, we will add an explicit mapping table and check the invariance of the relevant operators under this association. revision: yes

  2. Referee: [Functional quantization section] The functional quantization step that incorporates Gribov ambiguities and produces the symmetry violation is presented as following directly from the BRST framework, yet the manuscript does not display the explicit form of the modified measure or the horizon condition used. Without these intermediate expressions it is impossible to confirm that the reported violation is a direct consequence rather than an artifact of an unstated truncation.

    Authors: We appreciate the request for greater explicitness in the functional quantization section. The symmetry violation arises directly from incorporating the Gribov ambiguities through the horizon condition within the BRST framework, but we agree that displaying the modified measure and the explicit form of the horizon condition will allow readers to confirm this without ambiguity. We will include these intermediate expressions in the revised manuscript. revision: yes

Circularity Check

0 steps flagged

Derivation remains self-contained; no reduction of claims to inputs by construction.

full rationale

The paper performs explicit functional quantization of the FLPR model, generates BRST-related transformations from the discrete symmetries of the gauge-fixed action, and shows violation when Gribov ambiguities are incorporated. These steps rely on the model's Lagrangian, gauge-fixing procedure, and horizon condition as stated inputs rather than re-deriving them from the target result. The QCD connection is introduced only at the end via an explicit mapping of variables and fields, which functions as an interpretive analogy and does not enter the preceding derivations or force any equation by self-reference. No self-citations, fitted parameters renamed as predictions, or ansatzes smuggled through prior work appear as load-bearing elements in the chain. The analysis is therefore independent of the final interpretive step and does not exhibit circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review limits visibility into explicit axioms or parameters; standard BRST nilpotency and gauge-fixing assumptions are presumed but not enumerated here.

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