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arxiv: 2605.10416 · v1 · submitted 2026-05-11 · ✦ hep-th · hep-lat· hep-ph

Recognition: 2 theorem links

· Lean Theorem

Infrared spectra of some strongly--coupled chiral gauge theories

Stefano Bolognesi , Kenichi Konishi , Matteo Orso
Authors on Pith no claims yet

Pith reviewed 2026-05-12 05:04 UTC · model grok-4.3

classification ✦ hep-th hep-lathep-ph
keywords chiral gauge theoriesinfrared spectraanomaly matchinggeneralized symmetriesasymptotically free theoriesrenormalization group flowslight composite statesconfinement
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0 comments X

The pith

Chiral gauge theories with chosen gauge groups and fermion representations develop diverse infrared effective theories and light spectra.

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

The paper examines several asymptotically free chiral gauge theories whose only inputs are the gauge group, the representations of Weyl fermions, and the relative sizes of their strong-coupling scales. These models lack nontrivial nonabelian global symmetries. Using anomaly-matching conditions from generalized symmetries together with established results from vectorlike theories, the analysis maps out the resulting low-energy phases. A reader would care because the work shows that even simple chiral models can produce a range of confined or symmetry-broken infrared behaviors whose particle content is fixed by the input data.

Core claim

In these chiral gauge theories the infrared effective theories, renormalization-group flows, and light spectra turn out to be rich and varied. The dynamics are fixed by the choice of gauge group and matter representations together with the relative magnitudes of the renormalization-group-invariant scales associated with each group. Generalized symmetry arguments and anomaly matching, supplemented by lessons from QCD and supersymmetric Yang-Mills, determine the possible light composite states and the pattern of symmetry breaking or confinement in each case.

What carries the argument

Generalized symmetries combined with anomaly-matching conditions applied to asymptotically free chiral gauge theories that have no nontrivial nonabelian global symmetries.

If this is right

  • Different choices of gauge groups produce distinct infrared phases whose light-particle content is fixed by the anomaly constraints.
  • The relative magnitudes of the strong scales control the hierarchy of masses and the sequence of RG flows between different effective theories.
  • The absence of family-like global symmetries still permits a variety of confined or Higgs-like infrared regimes with specific composite fermions and bosons.
  • The resulting light spectra can be compared directly with expectations from vectorlike theories such as QCD.

Where Pith is reading between the lines

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

  • The same method could be applied to models that include multiple gauge factors to generate more elaborate mass hierarchies.
  • Lattice studies of the simplest cases would provide a direct test of whether the anomaly-matching predictions survive in the strong-coupling regime.
  • The patterns found here may serve as templates for constructing chiral sectors in extensions of the Standard Model.

Load-bearing premise

Generalized symmetries and anomaly matching determine the infrared dynamics and spectra of these specific chiral gauge theories.

What would settle it

An explicit computation or lattice simulation of one of the studied models that finds a different light spectrum or a different pattern of infrared phases than the one predicted by the anomaly-matching analysis would falsify the central claim.

Figures

Figures reproduced from arXiv: 2605.10416 by Kenichi Konishi, Matteo Orso, Stefano Bolognesi.

Figure 1
Figure 1. Figure 1: The RG flow of the coupling constants in the SU(N) − SU(N + 4) model of Table. 1. The top picture corresponds to the theory with N ≥ 5, the lower corresponds to N ≤ 4. Thus SU(N) ′ and SU(4) are both asymptotically-free, as long as N < 21, which we assume to be the case below. The system at the scale below Λ1 also contains 8N + 1 pseudo NG bosons in the case SU(N + 4) is a global symmetry. The 8N (would-be… view at source ↗
Figure 2
Figure 2. Figure 2: The RG flow of the system [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: A schematic view of the RG flow of the coupling constants in the quiver SU(N) 3 model. g1,2,3(µ) represent the coupling constants of SU(N)1, SU(N)2 and SU(N)3, respectively, as functions of the mass scale µ. At µ ≃ Λ1 the SU(N)1 interactions become strong, and assumed to confine and form the ψκ condensate, (3.3). The axial combination of SU(N)2 and SU(N)3 gets spontaneously broken and the corresponding gau… view at source ↗
Figure 4
Figure 4. Figure 4: a SU(N) n quiver model. When n is even, the system ends up with an SU(N)1−SU(N)2 quiver model in the infrared limit. When one of the SU(N) factors, say, SU(N)1, becomes strongly coupled at the mass scale Λ, it confines and all fermions get a dynamical mass of the order of Λ, producing massive mesons and baryons of mass ∼ Λ. Depending on the coupling gSU(N)2 near Λ, there may appear somewhat lighter broken … view at source ↗
Figure 5
Figure 5. Figure 5: Symmetries acting on the fermions. The two large ellipses including the sections (2467895) and (1367895) represent SU(6)L and SU(6)R transformations, respectively. The two smaller ellipses containing the sections (469) and (359) represent the subgroups Sp(6)L ⊂ SU(6)L and Sp(6)R ⊂ SU(6)R, respectively. The combined section (56789) represents the intersection SU(6)V = SU(6)L ∩ SU(6)R, while the section (9) … view at source ↗
Figure 6
Figure 6. Figure 6: The coupling constant flow of the SU(N) − Sp(6) − Sp(6) model of [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: The coupling constant RG flow of the SU(N) − Sp(6)L − Sp(6)R model of [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: The coupling constant RG flow of the SU(10) model assuming the breaking (5.8). Due to the large quadratic Casimir the breaking might happen when the coupling constant is still relatively small. The two unbroken subgroups are one AF and the other IF. phenomenon. Two of the SU(2) gauge bosons (“W-bosons”) get massive, with mass of the order of ∼ g2(Λ2)Λ2 , (5.17) while the third SU(2) gauge boson remains exa… view at source ↗
read the original abstract

Several simple asymptotically-free chiral gauge theories are studied. The only ``free parameters'' of our models are the choice of the gauge group and the matter Weyl fermion representations, and the relative magnitudes of the renormalization-group-invariant scales $\Lambda_i$ associated with each gauge group. None of our models has nontrivial nonabelian global symmetries (``family''--like fermion representations). We rely on some recent theoretical developments on the dynamics of strongly--coupled chiral gauge theories, based on the generalized symmetries and associated new types of anomaly-matching consideration, but also on the solid knowledge on vectorlike gauge theories such as QCD and supersymmetric Yang-Mills theories. The structures of the infrared effective theories, the RG flows, and the light spectra found in these models are surprisingly rich and intriguing.

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

1 major / 2 minor

Summary. The manuscript examines several simple asymptotically-free chiral gauge theories without nontrivial nonabelian global symmetries. The only inputs are the gauge group, Weyl fermion representations, and the relative magnitudes of the renormalization-group-invariant scales Λ_i. Drawing on generalized symmetries, anomaly matching, and analogies to vectorlike theories (QCD, supersymmetric Yang-Mills), the authors derive the structures of the infrared effective theories, the RG flows, and the light spectra, which they describe as surprisingly rich and intriguing.

Significance. If the anomaly-matching arguments and dynamical analogies hold, the work provides an exploratory but systematic catalog of IR behaviors in chiral gauge theories. The explicit treatment of relative Λ_i scales as inputs allows concrete predictions for spectra and flows that could guide lattice simulations or model-building efforts in strongly coupled regimes.

major comments (1)
  1. [Abstract] Abstract and introductory discussion of model construction: the relative magnitudes of the Λ_i scales are explicitly treated as free parameters that directly control the RG flows and resulting light spectra. This parameter dependence is load-bearing for the claim of rich and intriguing structures, since different orderings of the Λ_i can alter which composites remain light or which effective theories emerge; a dedicated subsection quantifying the sensitivity of the spectra to these ratios (or demonstrating robustness) is required.
minor comments (2)
  1. Ensure that all cited results on generalized symmetries and anomaly matching are accompanied by explicit references and brief statements of the relevant theorems or matching conditions used for each model.
  2. A summary table listing the gauge groups, representations, and chosen Λ_i hierarchies for each example would improve readability and allow readers to track the mapping from inputs to predicted spectra.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their careful review and constructive feedback on our manuscript. We address the major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract and introductory discussion of model construction: the relative magnitudes of the Λ_i scales are explicitly treated as free parameters that directly control the RG flows and resulting light spectra. This parameter dependence is load-bearing for the claim of rich and intriguing structures, since different orderings of the Λ_i can alter which composites remain light or which effective theories emerge; a dedicated subsection quantifying the sensitivity of the spectra to these ratios (or demonstrating robustness) is required.

    Authors: We appreciate the referee's point regarding the role of the relative Λ_i scales. In our analysis, we indeed treat these relative magnitudes as inputs and systematically consider the different possible orderings for each gauge theory model. This leads to the variety of IR behaviors and light spectra that we find intriguing. The different orderings correspond to distinct dynamical regimes, and we discuss the resulting effective theories and spectra for each case. While a continuous sensitivity analysis is not feasible or necessary given the exponential separation of scales, we agree that explicitly summarizing the dependence on the ordering in a dedicated subsection would improve clarity. We will add such a subsection in the revised version, tabulating the possible spectra for the main orderings considered. revision: yes

Circularity Check

0 steps flagged

No circularity: inputs explicitly declared and derivation relies on external anomaly matching plus known vectorlike results

full rationale

The paper states its only free parameters upfront (gauge group, Weyl representations, and relative Λ_i scales) and derives IR structures, RG flows, and spectra by applying generalized symmetries, anomaly-matching constraints, and analogies to established vectorlike theories (QCD, SYM). No step reduces a claimed prediction or uniqueness result to a fit of the target quantity itself, nor does any load-bearing premise collapse to a self-citation whose validity is presupposed by the present work. The analysis is therefore self-contained against its stated inputs and external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the choice of gauge groups and Weyl fermion representations, the relative magnitudes of the RG-invariant scales Λ_i as free parameters, and the applicability of generalized-symmetry anomaly-matching techniques from recent literature together with results from vectorlike theories.

free parameters (1)
  • relative magnitudes of Λ_i
    The relative sizes of the renormalization-group-invariant scales associated with each gauge group are free parameters that determine the RG flows and spectra.
axioms (2)
  • domain assumption Recent developments on generalized symmetries and anomaly-matching apply to the dynamics of the studied chiral gauge theories
    The paper relies on these developments to constrain the infrared spectra and effective theories.
  • domain assumption Knowledge from vectorlike gauge theories such as QCD and supersymmetric Yang-Mills informs the infrared structures of these chiral models
    Used as a solid base for interpreting the light spectra and RG flows.

pith-pipeline@v0.9.0 · 5429 in / 1407 out tokens · 62160 ms · 2026-05-12T05:04:23.209343+00:00 · methodology

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Reference graph

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