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arxiv: 1906.11445 · v1 · pith:JZIRIBOKnew · submitted 2019-06-27 · ✦ hep-ph

The infrared or ultraviolet scale for a gauge theory

Renata Jora This is my paper

Pith reviewed 2026-05-25 14:58 UTC · model grok-4.3

classification ✦ hep-ph
keywords gauge theoryintrinsic scalesupersymmetric GUTSO(10)SU(5)E6coupling constant divergence
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0 comments X

The pith

A conjecture allowing scale comparison between gauge theories in the same space-time volume identifies SO(10) as the only viable supersymmetric GUT among SU(5), SO(10), and E6.

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

The paper introduces a conjecture to find the intrinsic scale of any gauge theory, defined as the point where its coupling constant diverges, by comparing it directly to a second theory that has known phenomenological data, provided both theories occupy identical space-time volumes. The conjecture is first verified independently on U(1) electromagnetic theory and on QCD. When applied to the supersymmetric grand unified groups SU(5), SO(10), and E6, only SO(10) produces an intrinsic scale consistent with viability. The approach treats the intrinsic scale as a property fixed by the shared volume rather than by independent renormalization-group running alone.

Core claim

The group SO(10) is the only viable candidate among the supersymmetric GUT groups SU(5), SO(10) and E6, because the conjecture that equates intrinsic scales through direct comparison in the same space-time volume yields a consistent scale solely for SO(10).

What carries the argument

The conjecture that equates the intrinsic scale of any gauge theory to that of a reference theory by placing both in the same space-time volume.

If this is right

  • Only SO(10) satisfies the volume-comparison condition among the three supersymmetric GUT groups and therefore remains the sole candidate.
  • The same volume-comparison method can be used to assign intrinsic scales to any other gauge theory once a reference theory with known scale is fixed in the identical volume.
  • The verifications for U(1)em and QCD confirm that the conjecture reproduces known scales for both abelian and non-abelian theories.

Where Pith is reading between the lines

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

  • If the volume-equivalence conjecture holds beyond the tested cases, it could supply a parameter-free route to the Landau pole location for any gauge theory.
  • The requirement that two theories share the identical space-time volume might be tested by embedding both in a common finite-volume lattice simulation and comparing their extracted scales.

Load-bearing premise

The conjecture that the intrinsic scale of any gauge theory can be obtained by direct comparison to another theory placed in the same space-time volume is valid for the supersymmetric GUT groups under consideration.

What would settle it

An explicit calculation showing that the intrinsic scale obtained for SU(5) or E6 under the same volume condition matches the scale required by low-energy phenomenology while the SO(10) scale does not.

Figures

Figures reproduced from arXiv: 1906.11445 by Renata Jora.

Figure 1
Figure 1. Figure 1: FIG. 1: Plot of [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
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Figure 2. Figure 2: FIG. 2: Plot of [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
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Figure 3. Figure 3: FIG. 3: Plot of [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
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Figure 4. Figure 4: FIG. 4: Plot of [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
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Figure 5. Figure 5: FIG. 5: Plot of [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
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Figure 6. Figure 6: FIG. 6: Plot of [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
read the original abstract

We propose a conjecture that leads to the determination of the intrinsic scale (the scale at which the coupling constant diverges) for any gauge theory by comparison to another theory for which there is phenomenological information, provided that the two theories are placed in the same space-time volume. This conjecture is verified independently for $U(1)_{em}$ and for $QCD$. In this framework and from this perspective we show that the group $SO(10)$ is the only viable candidate among the supersymmetric GUT groups $SU(5)$, $SO(10)$ and $E_6$.

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 / 0 minor

Summary. The manuscript proposes a conjecture that the intrinsic scale of any gauge theory (the scale at which the coupling diverges) can be obtained by direct comparison to another theory placed in the same space-time volume. The conjecture is stated to be verified independently for U(1)_em and for QCD. Using this framework, the paper concludes that SO(10) is the only viable candidate among the supersymmetric GUT groups SU(5), SO(10), and E6.

Significance. If the conjecture holds and its application to supersymmetric GUTs is justified by independent checks, the work would supply a novel volume-based criterion for selecting GUT candidates and determining intrinsic scales across gauge theories. The approach is original in its use of phenomenological input from one theory to fix the scale of another via shared volume, but the significance is constrained by the absence of any supporting derivation or test for the GUT cases.

major comments (2)
  1. [Abstract] Abstract: the conjecture is asserted to be verified independently for U(1)_em and QCD, yet the manuscript supplies no derivation, data, error analysis, or consistency test showing why the volume-comparison procedure remains valid once the gauge group is enlarged to SU(5), SO(10), or E6, supersymmetry is imposed, and the representations become those of a GUT. This extrapolation is load-bearing for the central claim that SO(10) is the sole viable candidate.
  2. [GUT application section] GUT application section: the ranking of SU(5), SO(10), and E6 rests on the conjecture holding for these groups, but no analytic argument, lattice check, or cross-check is provided beyond the U(1) and QCD verifications; without that step the selection of SO(10) cannot be assessed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and the detailed comments on the manuscript. We respond to the major comments point by point below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the conjecture is asserted to be verified independently for U(1)_em and QCD, yet the manuscript supplies no derivation, data, error analysis, or consistency test showing why the volume-comparison procedure remains valid once the gauge group is enlarged to SU(5), SO(10), or E6, supersymmetry is imposed, and the representations become those of a GUT. This extrapolation is load-bearing for the central claim that SO(10) is the sole viable candidate.

    Authors: The conjecture is proposed as a general principle that applies to any gauge theory by means of volume comparison. The independent verifications for U(1)_em and QCD are presented to establish the procedure in those settings. The application to the supersymmetric GUT groups follows directly from the same conjecture without additional assumptions. No separate derivation or lattice test is supplied for the GUT cases because the manuscript advances the conjecture itself as the unifying framework; the GUT analysis is an application rather than an independent verification. revision: no

  2. Referee: [GUT application section] GUT application section: the ranking of SU(5), SO(10), and E6 rests on the conjecture holding for these groups, but no analytic argument, lattice check, or cross-check is provided beyond the U(1) and QCD verifications; without that step the selection of SO(10) cannot be assessed.

    Authors: The ranking of the GUT candidates is obtained by applying the volume-comparison procedure under the conjecture to each group. The manuscript does not supply further analytic arguments or lattice checks for SU(5), SO(10), or E6 because the work is framed as an exploration of the conjecture's consequences once it is accepted on the basis of the U(1) and QCD cases. We maintain that the selection of SO(10) follows logically from the conjecture as stated; additional cross-checks would constitute separate work beyond the present scope. revision: no

Circularity Check

0 steps flagged

No circularity; conjecture stated as independently verified before application to GUTs

full rationale

The paper proposes a conjecture for determining intrinsic scales via volume comparison, explicitly states that it 'is verified independently for U(1)em and for QCD', and only then applies the same framework to rank SU(5), SO(10) and E6. No quoted step shows the verification itself being performed by fitting the very scales under test, no self-citation chain is load-bearing, and no equation reduces a GUT-scale prediction to a fitted input by construction. The derivation therefore remains self-contained against the stated external benchmarks; any concern about extrapolation validity is a question of justification, not circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper's central claim rests on a single ad-hoc conjecture introduced in the abstract; no free parameters, standard mathematical axioms, or invented entities are mentioned.

axioms (1)
  • ad hoc to paper The intrinsic scale of a gauge theory can be determined by comparison to another theory in the same space-time volume.
    This is the conjecture proposed in the abstract.

pith-pipeline@v0.9.0 · 5609 in / 1192 out tokens · 26863 ms · 2026-05-25T14:58:25.743351+00:00 · methodology

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Reference graph

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