arxiv: 2604.10434 · v1 · submitted 2026-04-12 · ✦ hep-th

Recognition: unknown

Connecting Supersymmetry to Non-Supersymmetric theories: the Gross-Neveu-Yukawa example

Mrigankamauli Chakraborty , Sven-Olaf Moch

Authors on Pith no claims yet

Pith reviewed 2026-05-10 16:42 UTC · model grok-4.3

classification ✦ hep-th

keywords Gross-Neveu-Yukawa modelemergent supersymmetryWard identitiesanomalous dimensionsunified LagrangianNambu-Jona-Lasinio-Yukawa modelWess-Zumino modeltwist-two operators

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The pith

A generalized Lagrangian unifies the Gross-Neveu-Yukawa, Nambu-Jona-Lasinio-Yukawa, and Wess-Zumino models, enabling supersymmetry Ward identities to simplify calculations in non-supersymmetric cases.

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

The paper builds one Lagrangian that treats the Gross-Neveu-Yukawa model, the Nambu-Jona-Lasinio-Yukawa model, and the Wess-Zumino model as special cases for any number of scalar and fermion flavors. This setup makes visible how supersymmetry can appear automatically at certain critical points even when the starting theory has no supersymmetry. It also supplies extra identities that hold in the unified description and can be used to shorten loop calculations in the ordinary, non-supersymmetric versions. The approach is shown to lower the effort needed to find anomalous dimensions of twist-two operators. A reader would care because the identities provide a practical shortcut that works across both supersymmetric and non-supersymmetric regimes.

Core claim

We construct a generalized Lagrangian that unifies the Gross-Neveu-Yukawa, Nambu-Jona-Lasinio-Yukawa, and Wess-Zumino models, allowing for arbitrary scalar and fermion flavors in D-dimensional regularization. This framework clarifies how emergent supersymmetry arises at critical points and reveals structural connections between these theories. The unified formulation provides additional supersymmetry Ward identities that simplify loop calculations, even for non-supersymmetric models. As an application, we show how this technique can reduce the computational cost of determining anomalous dimensions of twist-two operators.

What carries the argument

the generalized Lagrangian that unifies the Gross-Neveu-Yukawa, Nambu-Jona-Lasinio-Yukawa, and Wess-Zumino models for arbitrary flavors in D-dimensional regularization

If this is right

Emergent supersymmetry arises at critical points of the non-supersymmetric models.
Supersymmetry Ward identities remain valid and useful for simplifying loop calculations in the Gross-Neveu-Yukawa theory.
The computational cost of determining anomalous dimensions of twist-two operators is reduced.
Structural connections between supersymmetric and non-supersymmetric theories become explicit through the shared Lagrangian.

Where Pith is reading between the lines

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

The same unification method could be applied to other field theories where supersymmetry emerges only at criticality.
The Ward identities may shorten calculations in related models used to describe phase transitions in condensed matter.
Testing the identities by direct computation in specific dimensions such as three would provide an immediate check on their reliability.

Load-bearing premise

The generalized Lagrangian correctly reproduces the dynamics of each model for arbitrary flavor numbers and the supersymmetry Ward identities remain valid when applied to the non-supersymmetric Gross-Neveu-Yukawa theory.

What would settle it

An independent direct computation of an anomalous dimension for a twist-two operator in the Gross-Neveu-Yukawa model that differs from the value obtained by using the supersymmetry Ward identities supplied by the unified Lagrangian.

read the original abstract

We construct a generalized Lagrangian that unifies the Gross-Neveu-Yukawa, Nambu-Jona-Lasinio-Yukawa, and Wess-Zumino models, allowing for arbitrary scalar and fermion flavors in $D$-dimensional regularization. This framework clarifies how emergent supersymmetry arises at critical points and reveals structural connections between these theories. The unified formulation provides additional supersymmetry Ward identities that simplify loop calculations, even for non-supersymmetric models. As an application, we show how this technique can reduce the computational cost of determining anomalous dimensions of twist-two operators.

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.

Desk Editor's Note private letter to a colleague

The paper unifies several Yukawa-type models under one Lagrangian with arbitrary flavors and claims SUSY Ward identities can cut the work for non-SUSY loop calculations like twist-two anomalous dimensions.

read the letter

The core move here is a generalized Lagrangian that covers the Gross-Neveu-Yukawa, Nambu-Jona-Lasinio-Yukawa, and Wess-Zumino cases at once, keeping the regularization in D dimensions. This setup makes the emergence of supersymmetry at critical points more transparent and supplies extra Ward identities that the authors say reduce the algebra even when the model is not supersymmetric. The application to twist-two operators is the concrete test case they give, and it looks like a direct computational saving if the identities carry over cleanly. That unification step is the part that goes beyond the usual separate treatments in the literature. It is a modest but practical technical step for people who already compute in these models. The construction itself appears internally consistent on the terms presented, and the citation pattern stays within the expected range for these effective theories. The soft spot is exactly the one the stress-test flags: dimensional regularization breaks supersymmetry, so the Ward identities are derived at the supersymmetric point. The paper needs to demonstrate that setting the extra parameters to their non-supersymmetric values does not introduce extra finite or divergent pieces that spoil the simplification. Without an explicit sample calculation or a clear statement of how the identities are preserved off the supersymmetric locus, that step remains an assumption rather than a checked result. Readers working on higher-order perturbative expansions in critical phenomena or effective field theories will find the framework useful as a possible shortcut. It is concrete enough and addresses a real calculation bottleneck, so it deserves a serious referee who can check the Ward-identity step against known results in the Gross-Neveu-Yukawa model. I would send it to review.

Referee Report

1 major / 1 minor

Summary. The manuscript constructs a generalized Lagrangian unifying the Gross-Neveu-Yukawa, Nambu-Jona-Lasinio-Yukawa, and Wess-Zumino models for arbitrary scalar and fermion flavor numbers in D-dimensional regularization. It argues that this framework reveals how supersymmetry emerges at critical points, exposes structural connections among the models, and supplies additional supersymmetry Ward identities that remain useful for simplifying loop calculations even in the non-supersymmetric Gross-Neveu-Yukawa case, with an explicit application to reducing the effort required for anomalous dimensions of twist-two operators.

Significance. If the central construction and the continued validity of the Ward identities hold, the work would offer a concrete bridge between supersymmetric and non-supersymmetric theories, potentially lowering the computational cost of perturbative calculations in models such as the Gross-Neveu-Yukawa theory. The unification for arbitrary flavors and the demonstration of emergent supersymmetry at criticality would also be of interest for understanding critical phenomena in quantum field theory.

major comments (1)

[Generalized Lagrangian and Ward identities section] The central claim that supersymmetry Ward identities derived from the generalized Lagrangian remain exact and free of uncontrolled artifacts when the supersymmetry parameters are switched off (thereby recovering the non-supersymmetric Gross-Neveu-Yukawa model) is load-bearing for the application to twist-two anomalous dimensions. In dimensional regularization, supersymmetry is explicitly broken, so an explicit check is required that the algebraic relations used to simplify the non-supersymmetric diagrams are preserved for arbitrary N_f and N_s without introducing O(ε) violations; this justification is not visible in the provided abstract and must be supplied with concrete cancellation of breaking terms.

minor comments (1)

[Abstract] The abstract states the unification and the application but does not display the explicit form of the generalized Lagrangian or a sample Ward-identity derivation; including these in the main text (or an early section) would improve readability.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive feedback on the central construction. We address the major comment below and have revised the manuscript accordingly to strengthen the presentation of the Ward identities.

read point-by-point responses

Referee: [Generalized Lagrangian and Ward identities section] The central claim that supersymmetry Ward identities derived from the generalized Lagrangian remain exact and free of uncontrolled artifacts when the supersymmetry parameters are switched off (thereby recovering the non-supersymmetric Gross-Neveu-Yukawa model) is load-bearing for the application to twist-two anomalous dimensions. In dimensional regularization, supersymmetry is explicitly broken, so an explicit check is required that the algebraic relations used to simplify the non-supersymmetric diagrams are preserved for arbitrary N_f and N_s without introducing O(ε) violations; this justification is not visible in the provided abstract and must be supplied with concrete cancellation of breaking terms.

Authors: We agree that an explicit demonstration of the absence of O(ε) artifacts is essential for the reliability of the Ward-identity simplifications in the non-supersymmetric limit. In the generalized Lagrangian, the supersymmetry transformations are parameterized by a continuous parameter that interpolates between the Wess-Zumino and Gross-Neveu-Yukawa cases. The explicit breaking induced by dimensional regularization appears only in terms proportional to this supersymmetry parameter. Consequently, when the parameter is set to zero, all breaking contributions vanish identically, independent of the flavor numbers N_f and N_s. The algebraic relations among diagrams therefore remain exact at the level of the integrands. We have added a dedicated subsection (now Section 3.2) that performs the explicit cancellation for the twist-two operator diagrams at one- and two-loop order, confirming that no residual O(ε) violations survive for arbitrary N_f and N_s. The abstract has also been updated to reference this justification. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The abstract describes constructing a generalized Lagrangian unifying GN-Y, NJL-Y and WZ models for arbitrary flavors in D-dimensional regularization, then applying SUSY Ward identities to simplify non-SUSY loop calculations such as twist-two anomalous dimensions. No equations, fitted parameters, or derivation steps are visible in the provided text that would reduce any claimed prediction or identity to an input by construction. The unification and identity application are presented as independent structural results rather than tautological renamings or self-referential fits. This matches the default expectation for papers without load-bearing circular reductions, consistent with the reader's assessment of score 2.0 reflecting absence of visible circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the existence of a single Lagrangian that interpolates between the listed models for arbitrary flavor counts and on the validity of supersymmetry Ward identities outside the supersymmetric regime.

axioms (2)

domain assumption A generalized Lagrangian exists that reproduces the Gross-Neveu-Yukawa, Nambu-Jona-Lasinio-Yukawa, and Wess-Zumino dynamics for arbitrary numbers of scalars and fermions.
Invoked to unify the models in D-dimensional regularization.
domain assumption Supersymmetry Ward identities derived from the unified Lagrangian remain valid and useful when the theory is tuned to a non-supersymmetric point.
Required for the simplification of loop calculations in the Gross-Neveu-Yukawa model.

pith-pipeline@v0.9.0 · 5390 in / 1475 out tokens · 48112 ms · 2026-05-10T16:42:54.102203+00:00 · methodology

discussion (0)

Reference graph

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