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A square-lattice realization of equation-of-motion flow extends boundary gauge fields into a disk while preserving gauge invariance.

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2026-06-28 02:34 UTC pith:WJB3YOJS

load-bearing objection This is a concrete lattice proposal for the disk flow plus anomaly inflow demo, but the abstract leaves the actual checks invisible so the claims stay unverified for now.

arxiv 2606.05305 v3 pith:WJB3YOJS submitted 2026-06-03 hep-lat hep-phhep-thnucl-th

Gauge field flow for chiral gauge theories on a disk boundary

Jinlong Dang , Rohith Karur , Srimoyee Sen This is my paper
classification hep-lat hep-phhep-thnucl-th
keywords chiral gauge theorieslattice gauge theoryanomaly inflowdisk manifoldequation of motion flowgauge field extensionboundary fermions
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper develops a method to extend gauge field configurations from the boundary of a disk into its interior using an equation-of-motion flow on a square lattice. This construction maintains the gauge invariance required for 2n-dimensional chiral gauge theories. Coupling the resulting flow gauge field to fermions on the lattice shows how boundary anomalies are canceled through inflow from the bulk. This approach provides a concrete lattice setup for studying chiral gauge theories non-perturbatively.

Core claim

A concrete realization of the equation of motion flow embeds the disk on a square lattice and extends boundary gauge configurations into the interior while preserving 2n-dimensional gauge invariance. When coupled to fermions, this demonstrates anomaly inflow and cancellation at work on the lattice.

What carries the argument

The equation-of-motion flow prescription, which extends boundary gauge configurations into the disk interior.

Load-bearing premise

The chosen flow prescription extends boundary gauge configurations into the disk interior while preserving 2n-dimensional gauge invariance on the square lattice.

What would settle it

A numerical simulation where the flowed gauge field violates gauge invariance or where the anomaly cancellation does not hold for the coupled fermions.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • This enables non-perturbative simulations of chiral gauge theories on the lattice.
  • Anomaly inflow from the bulk cancels boundary anomalies for the fermions.
  • The method works with the disk embedded on a square lattice.
  • Preservation of gauge invariance holds throughout the flow.

Where Pith is reading between the lines

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

  • This lattice construction could be tested numerically by measuring anomaly cancellation in specific models.
  • Extensions to other manifold geometries might follow similar flow prescriptions.
  • The approach may inform simulations of the standard model with chiral fermions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

0 major / 3 minor

Summary. The manuscript proposes a concrete lattice realization of the equation-of-motion flow that extends boundary gauge configurations into the interior of a (2n+1)-dimensional disk manifold embedded on a square lattice. It then couples the resulting flow gauge field to fermions and demonstrates the mechanisms of anomaly inflow and anomaly cancellation at work on the lattice.

Significance. If the construction is correct, the work supplies an explicit, non-perturbative lattice prescription for realizing chiral gauge theories via a disk geometry, together with a direct numerical illustration of anomaly inflow. Such a concrete implementation addresses a key technical requirement in recent formulations of lattice chiral fermions and could enable further studies of anomaly cancellation in this setting.

minor comments (3)
  1. The abstract states that the flow 'preserves 2n dimensional gauge invariance,' but the manuscript should include an explicit verification (analytic or numerical) that the chosen lattice embedding of the disk and the EOM flow definition maintain this invariance at finite lattice spacing; this would strengthen the central claim.
  2. When the flow gauge field is coupled to fermions, the demonstration of anomaly inflow would benefit from a quantitative measure (e.g., a lattice index or spectral flow observable) rather than a purely qualitative illustration, to make the cancellation mechanism falsifiable.
  3. Notation for the disk embedding and the precise discretization of the EOM flow should be introduced with a short table or diagram early in the text to aid readability for readers unfamiliar with the disk-boundary approach.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive summary, assessment of significance, and recommendation of minor revision. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity; proposal is a new lattice construction

full rationale

The paper describes a concrete proposal for realizing equation-of-motion flow on a square lattice disk and a demonstration of anomaly inflow/cancellation when coupling to fermions. No quoted equations or steps reduce by construction to fitted inputs, self-definitions, or self-citation chains. The abstract and description present an independent construction whose validity rests on explicit lattice implementation rather than renaming or re-deriving prior results. This matches the default non-circular outcome for a methods paper.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract only; no explicit free parameters, axioms, or invented entities are visible in the provided text.

pith-pipeline@v0.9.1-grok · 5628 in / 999 out tokens · 45280 ms · 2026-06-28T02:34:46.315334+00:00 · methodology

0 comments
read the original abstract

A recent non-perturbative formulation of $2n$ dimensional chiral gauge theories relies on realizing chiral fermions on the $2n$ dimensional boundary of a $2n+1$ dimensional disk manifold. It also requires extending boundary gauge configurations into the interior of the disk using some flow prescription that preserves 2n dimensional gauge invariance. In this paper we propose a concrete realization of the equation of motion flow with the disk embedded on a square lattice. In addition, we couple the flow gauge field to fermions and demonstrate the mechanism of anomaly inflow and anomaly cancellation at work on the lattice.

Figures

Figures reproduced from arXiv: 2606.05305 by Jinlong Dang, Rohith Karur, Srimoyee Sen.

Figure 1
Figure 1. Figure 1: FIG. 1: Lattice gauge field prescription: we show 8 [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Gauge fields at [PITH_FULL_IMAGE:figures/full_fig_p008_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Currents at [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Electromagnetic fields at [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Two dimensional divergence summed over the [PITH_FULL_IMAGE:figures/full_fig_p009_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Rate of change of total charge in the interior, [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗

discussion (0)

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Forward citations

Cited by 1 Pith paper

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    hep-lat 2026-06 unverdicted novelty 6.0

    Implements gradient flow and EOM flow for gauge fields in n=1 domain wall fermion slab geometry on the lattice, demonstrating current conservation and anomaly inflow with background fields.

Reference graph

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