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arxiv: 2606.02708 · v1 · pith:PN5XMQ4Onew · submitted 2026-06-01 · ✦ hep-th · hep-ph

Supersymmetry, Large Extra Dimensions and the Gravitino Conjecture

Leonardo Bersigotti , Dieter Lust , Marco Scalisi This is my paper

Pith reviewed 2026-06-28 13:16 UTC · model grok-4.3

classification ✦ hep-th hep-ph
keywords supersymmetryextra dimensionsgravitino conjectureKaluza-Klein scaleType II compactificationsgauge mediationgravity mediationanisotropy exponent
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0 comments X

The pith

The linear relation between gravitino mass and Kaluza-Klein scale holds only for one or two large extra dimensions.

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

The paper examines whether the lack of signals for supersymmetry and extra dimensions can be understood as linked phenomena under the Gravitino Conjecture in Type II string compactifications. It parametrizes the internal volume scaling via an anisotropy exponent α that describes how the full volume relates to a large p-cycle, then derives the resulting contributions to the Kähler potential. This produces constraints on the scaling exponent n that ties the gravitino mass to the Kaluza-Klein scale and on the effective number of large dimensions αp. The analysis shows that n equals 1 only when one or two large extra dimensions are present, the sizes still reachable by micron-scale experiments. In those cases micron-sized dimensions correspond to a light gravitino and gauge-mediated breaking, while gravity mediation requires compactification scales outside current reach.

Core claim

Assuming the Gravitino Conjecture, in four-dimensional N=1 supergravity from Type II compactifications with large extra dimensions, parametrizing the scaling of the full internal volume with respect to a large p-cycle through an anisotropy exponent α leads to volume contributions in the Kähler potential that constrain the scaling exponent n relating the gravitino mass to the KK scale, with the result that the linear relation n=1 is compatible only with one or two large extra dimensions.

What carries the argument

The anisotropy exponent α that parametrizes volume scaling of the full internal space relative to a large p-cycle and thereby fixes the volume terms in the Kähler potential used to derive the exponent n linking gravitino mass to KK scale.

If this is right

  • Micron-sized extra dimensions imply a light gravitino.
  • Gauge-mediated supersymmetry breaking occurs in scenarios with one or two large extra dimensions.
  • Gravity mediation requires compactification scales beyond current experimental reach.
  • Only one or two large extra dimensions remain compatible with the linear scaling n=1.

Where Pith is reading between the lines

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

  • Future micron-scale gravity tests could directly constrain possible supersymmetry-breaking mediation mechanisms.
  • The correlation suggests that null results in both supersymmetry searches and extra-dimension searches may reinforce each other rather than being independent.
  • If the number of large dimensions exceeds two, the required nonlinear scaling would point to different volume hierarchies or mediation patterns not covered by n=1.

Load-bearing premise

The Gravitino Conjecture holds and supplies a direct relation between gravitino mass and Kaluza-Klein scale through volume scaling.

What would settle it

Observation of three or more large extra dimensions at micron scales together with a gravitino mass that violates the linear n=1 relation, or detection of gauge-mediated breaking at a scale incompatible with micron-sized dimensions.

read the original abstract

We investigate whether the absence of experimental signals for supersymmetry and extra dimensions can be understood as a correlated phenomenon. Assuming the Gravitino Conjecture, we study the relation between the gravitino mass and the Kaluza-Klein scale in four-dimensional $\mathcal{N}=1$ supergravity from Type II compactifications with large extra dimensions. We parametrize the scaling of the full internal volume with respect to that of a large $p$-cycle through an anisotropy exponent $\alpha$, and derive the corresponding volume contributions to the K\"ahler potential. This leads to constraints on the scaling exponent $n$, linking the gravitino mass to the KK scale, and on the effective number $\alpha p$ of large dimensions. We find that the linear relation $n=1$ is compatible only with one or two large extra dimensions, precisely the cases that can still be probed at micron distances. In such scenarios, micron-sized extra dimensions imply a light gravitino and gauge-mediated supersymmetry breaking, whereas gravity mediation corresponds to compactification scales beyond current experimental reach.

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

0 major / 1 minor

Summary. The manuscript assumes the Gravitino Conjecture and studies the relation between the gravitino mass and the Kaluza-Klein scale in 4D N=1 supergravity arising from Type II compactifications with large extra dimensions. It introduces an anisotropy exponent α to parametrize how the full internal volume scales relative to the volume of a large p-cycle, derives the resulting volume contributions to the Kähler potential, and obtains constraints on the scaling exponent n (linking m_{3/2} to the KK scale) together with the effective number αp of large dimensions. The principal result is that the linear relation n=1 is compatible only with one or two large extra dimensions—the cases still accessible to micron-scale probes—implying a light gravitino and gauge-mediated supersymmetry breaking in those scenarios.

Significance. If the Gravitino Conjecture holds, the work supplies a geometric mechanism that correlates the non-observation of supersymmetry with the non-observation of large extra dimensions. It yields concrete, experimentally falsifiable statements: micron-sized extra dimensions would require a light gravitino and gauge mediation, while gravity mediation would push the compactification scale beyond current reach. The explicit use of volume scaling with anisotropy exponent α to constrain n and αp from the Kähler potential is a clear strength; the resulting bounds are derived rather than fitted and remain testable by future extra-dimension searches.

minor comments (1)
  1. [Abstract] The abstract states that volume contributions 'lead to constraints on the scaling exponent n' but does not indicate the intermediate algebraic steps; a one-sentence outline of the scaling relation in the abstract would improve readability without lengthening the text.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of our manuscript, including the clear summary of our results on the Gravitino Conjecture in Type II compactifications with large extra dimensions, and for the recommendation to accept. No major comments were raised that require a response or changes to the paper.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper assumes the Gravitino Conjecture as an external input and parametrizes the internal volume scaling via an anisotropy exponent α to derive volume contributions to the Kähler potential in Type II compactifications. This leads to constraints on the scaling exponent n and effective number αp of large dimensions. The derivation is self-contained: α and n are introduced as free parameters whose compatibility with n=1 is checked against the assumed conjecture and volume scaling relations, without any reduction of outputs to fitted inputs by construction, self-definitional loops, or load-bearing self-citations that collapse the result to prior unverified claims by the same authors.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The paper introduces parametrization parameters α and n as part of the model setup to derive constraints, relying on the Gravitino Conjecture as the key assumption from prior literature; no new entities are postulated.

free parameters (2)
  • anisotropy exponent α
    Introduced to parametrize the scaling of the full internal volume with respect to that of a large p-cycle.
  • scaling exponent n
    Introduced to link the gravitino mass to the KK scale, with constraints derived on its possible values.
axioms (1)
  • domain assumption Gravitino Conjecture holds
    Assumed throughout to study the relation between gravitino mass and KK scale in the compactifications.

pith-pipeline@v0.9.1-grok · 5713 in / 1549 out tokens · 40430 ms · 2026-06-28T13:16:43.972723+00:00 · methodology

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Reference graph

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