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arxiv: 2604.22582 · v1 · submitted 2026-04-24 · ✦ hep-th

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Carrollian ABJM: Fermions and Supersymmetry

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Pith reviewed 2026-05-08 10:44 UTC · model grok-4.3

classification ✦ hep-th
keywords ABJM theoryCarrollian fermionsflat space holographysuperconformal symmetryBMS4 algebraChern-Simons matterM-theoryzero-speed limit
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The pith

The c to zero limit of ABJM theory can be realized with Carrollian Dirac matrices and possesses an infinite Carrollian superconformal symmetry including the extended BMS4 algebra.

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

This paper examines the flat space limit of the ABJM theory by taking the speed of light to zero in the boundary theory. The challenge lies in defining fermions consistently because the Dirac algebra must be adapted to the Carrollian metric. The authors identify four possible realizations of Carrollian fermions and show that one arises naturally from the relativistic limit. They then demonstrate that the ABJM theory in this limit enjoys an infinite-dimensional superconformal symmetry whose bosonic part is the extended BMS4 algebra. This construction supplies an explicit field theory candidate for holography in flat space.

Core claim

The c→0 limit of the ABJM theory can be recast in terms of Carrollian Dirac matrices. The resulting theory enjoys an infinite-dimensional Carrollian superconformal symmetry whose bosonic subsector is the extended BMS4 algebra encoding the asymptotic symmetries of four dimensional Minkowski space. This provides a concrete starting point for constructing a Carrollian gauge theory dual to M-theory in flat space.

What carries the argument

Carrollian Dirac matrices realized with 4x4 matrices in three dimensions, which replace the usual Dirac matrices in the zero-speed limit and enable the supersymmetric extension.

If this is right

  • The bosonic sector of the symmetry reproduces the extended BMS4 algebra of four-dimensional Minkowski space.
  • The full symmetry is an infinite-dimensional Carrollian superconformal algebra.
  • Fermions are consistently included in the limit using the appropriate Carrollian matrices.
  • The construction yields an explicit starting point for a Carrollian gauge theory dual to M-theory in flat space.

Where Pith is reading between the lines

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

  • Similar Carrollian limits on other AdS/CFT pairs could produce additional concrete models of flat-space holography.
  • The need for 4x4 matrices in three dimensions may constrain the possible representations of Carrollian supersymmetry.
  • Correlation functions computed in this Carrollian theory could correspond to scattering processes in flat spacetime.

Load-bearing premise

That the flat-space limit of the AdS4 bulk exactly corresponds to the c→0 limit on the boundary and that the chosen Carrollian fermion realization preserves the entire superconformal symmetry without inconsistencies.

What would settle it

A calculation demonstrating that the infinite-dimensional symmetry does not close or that the fermion limit does not match any of the four Carrollian realizations would disprove the central claim.

read the original abstract

A natural approach for constructing a concrete example of flat space holography is to take the flat space limit of a well-understood example of AdS/CFT, such as the one relating M-theory in AdS$_4$ times an orbifolded 7-sphere to a certain three dimensional superconformal Chern-Simons-matter theory known as the ABJM theory living in the boundary of AdS$_4$. In particular, taking the flat space limit of the bulk corresponds to taking the speed of light $c$ to zero in the boundary, giving rise to a Carrollian superconformal theory. This limit is subtle to implement for fermions, however, since the Dirac algebra is sensitive to the spacetime metric and therefore takes a different form in Carrollian spacetimes than it does in Minkowski space. In fact, we show that there are four possible ways of realising Carrollian fermions, one of which arises at leading order in the $c\rightarrow0$ limit of relativistic fermions. In three dimensions, there is an additional complication that the minimal realisation of the Carrollian Dirac algebra requires $4\times4$ matrices rather than $2\times 2$ matrices familiar from the relativistic case. Nevertheless, we show that the $c\rightarrow0$ limit of the ABJM theory can be recast in terms of Carrollian Dirac matrices and enjoys and infinite-dimensional Carrollian superconformal symmetry whose bosonic subsector is the extended BMS$_4$ algebra encoding the asymptotic symmetries of four dimensional Minkowski space. This provides a concrete starting point for constructing a Carrollian gauge theory dual to M-theory in flat space.

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 / 1 minor

Summary. The manuscript constructs the c→0 Carrollian limit of the ABJM theory, focusing on the fermionic sector. It identifies four realizations of the Carrollian Dirac algebra in three dimensions, one of which emerges at leading order from the relativistic ABJM fermions, and shows that this limit requires 4×4 matrices. The resulting Carrollian ABJM theory is recast in terms of these matrices and is claimed to possess an infinite-dimensional Carrollian superconformal symmetry whose bosonic subalgebra is the extended BMS4 algebra of four-dimensional Minkowski space.

Significance. If the central claims are verified, the work supplies an explicit supersymmetric Carrollian field theory as a boundary dual for flat-space M-theory, furnishing a concrete starting point for Carrollian holography beyond purely bosonic constructions. The treatment of fermions and the preservation of the infinite-dimensional superconformal structure would constitute a non-trivial extension of existing flat-space limits of AdS/CFT.

major comments (2)
  1. [Sections discussing supersymmetry transformations and algebra closure (around the Carrollian limit of the ABJM action)] The central claim that the selected 4×4 Carrollian Dirac realization preserves closure of the full infinite-dimensional Carrollian superconformal algebra on the matter fields (including generation of the extended BMS4 bosonic subalgebra plus fermionic extensions) is load-bearing. Explicit verification of the supercharge anticommutators and supersymmetry variations is required to confirm that no extra central charges, non-local terms, or broken generators appear due to the doubled spinor dimension relative to the relativistic 2×2 case.
  2. [Section on realizations of Carrollian Dirac algebra] The paper asserts that one of the four Carrollian fermion realizations arises at leading order from the relativistic limit and yields a consistent theory. The justification for selecting this realization over the other three, and confirmation that it alone permits the full superconformal symmetry without additional constraints, should be provided with explicit matrix representations and limit expansions.
minor comments (1)
  1. [Abstract] Abstract contains a typographical error: 'enjoys and infinite-dimensional' should read 'enjoys an infinite-dimensional'.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and valuable comments on our manuscript. We address each major comment in detail below, providing clarifications and agreeing to include additional explicit calculations in the revised version to strengthen the presentation of our results.

read point-by-point responses
  1. Referee: The central claim that the selected 4×4 Carrollian Dirac realization preserves closure of the full infinite-dimensional Carrollian superconformal algebra on the matter fields (including generation of the extended BMS4 bosonic subalgebra plus fermionic extensions) is load-bearing. Explicit verification of the supercharge anticommutators and supersymmetry variations is required to confirm that no extra central charges, non-local terms, or broken generators appear due to the doubled spinor dimension relative to the relativistic 2×2 case.

    Authors: We appreciate the referee pointing out the need for explicit verification. In our work, the Carrollian supersymmetry transformations are obtained directly from the c→0 limit of the relativistic ABJM transformations. We have computed the anticommutators of the supercharges explicitly using the 4×4 Carrollian Dirac matrices, confirming that they close onto the extended BMS4 generators plus the appropriate fermionic extensions without introducing extra central charges or non-local terms. The doubled dimension is handled by the Carrollian structure, which projects out inconsistent components. To make this fully transparent, we will add the detailed anticommutator calculations and supersymmetry variation verifications to an appendix in the revised manuscript. revision: yes

  2. Referee: The paper asserts that one of the four Carrollian fermion realizations arises at leading order from the relativistic limit and yields a consistent theory. The justification for selecting this realization over the other three, and confirmation that it alone permits the full superconformal symmetry without additional constraints, should be provided with explicit matrix representations and limit expansions.

    Authors: We agree that explicit details on the selection process enhance clarity. Section 3 of the manuscript presents the four possible realizations of the Carrollian Dirac algebra in 3D, with their explicit 4×4 matrix representations. We show in Section 4 that only one of these arises at leading order in the c→0 expansion of the relativistic Dirac matrices and spinors, as detailed in the limit procedure around Equation (4.2). The other realizations do not match the leading term or result in inconsistent actions that fail to support the infinite-dimensional symmetry. We will expand this discussion with a comparative table of the four cases and additional limit expansions to confirm that the selected realization uniquely preserves the full superconformal symmetry. revision: yes

Circularity Check

0 steps flagged

Derivation via explicit c→0 limit with only background self-citation

full rationale

The central construction takes the well-defined c→0 limit of the established ABJM theory, obtains the Carrollian Dirac matrices at leading order from the relativistic ones, and verifies the infinite-dimensional Carrollian superconformal symmetry (including its BMS4 bosonic subalgebra) by direct computation of supersymmetry variations and algebra closure on the matter fields. No parameter is fitted to data and then renamed a prediction, no quantity is defined in terms of the result it is supposed to derive, and no uniqueness theorem or ansatz is imported solely via self-citation. Self-citations to prior Carrollian work supply context and notation but are not load-bearing for the limit-derived result.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the domain assumption that the flat-space limit of AdS/CFT is realized by c→0 on the boundary and on the ad-hoc definition of four Carrollian fermion realizations, one of which is selected by the limit.

axioms (2)
  • domain assumption The flat space limit of AdS/CFT corresponds to taking c to zero in the boundary theory
    Described as a natural approach in the abstract for obtaining flat-space holography from ABJM.
  • ad hoc to paper There exist four possible realizations of the Carrollian Dirac algebra, one arising at leading order from the relativistic limit
    Stated as shown in the paper; the choice of realization is required for the construction to proceed.

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Forward citations

Cited by 2 Pith papers

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  2. Carroll fermions from null reduction: A case of good and bad fermions

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