Exploring Fragmented Supersymmetry: An Emerging Approach to Gravity and SUSY

Hello everyone,

I wanted to share an idea I’ve been exploring and get feedback from the community. This is a conceptual and exploratory approach, so I appreciate any critiques, suggestions, or references.

1. Motivation

Supersymmetry (SUSY) is elegant, but it has not yet been observed experimentally. I wondered: what if SUSY is not global or perfect, but emerges as an average of locally asymmetric fragments?

This led me to imagine a “broken mirror,” where classical symmetry only appears when we observe many regions at once. This idea could also reinterpret how gravity emerges collectively from local structures.

2. Toy Model: Discrete Fragments and Local Breaking

I considered a discrete space of fragments xix_ixi with a local breaking parameter ϵ(xi)∈[0,1]\epsilon(x_i) \in [0,1]ϵ(xi)∈[0,1].

Each fragment contributes with a momentum Pμ(xi)P_\mu(x_i)Pμ(xi), and its correlation with other fragments is given by f(xi,xj)f(x_i, x_j)f(xi,xj).

The emergent effective curvature is calculated as a weighted average over fragments:

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where:

• κ\kappaκ → coupling constant

• f(xi,xj)=exp⁡(−∣xi−xj∣2ℓc2)(1−ϵ(xi))(1−ϵ(xj))f(x_i, x_j) = \exp\Big(-\frac{|x_i - x_j|^2}{\ell_c^2}\Big) (1-\epsilon(x_i))(1-\epsilon(x_j))f(xi,xj)=exp(−ℓc2∣xi−xj∣2)(1−ϵ(xi))(1−ϵ(xj))

• ℓc\ell_cℓc → coherence scale

3. Visual Results

I generated a 1D toy model with 20 fragments to illustrate the concept:

# Fragment epsilons
epsilon = [0.3745, 0.9507, 0.7320, 0.5987, 0.1560, 0.1560, 0.0581, 0.8662, 0.6011, 0.7081,
 0.0206, 0.9699, 0.8324, 0.2123, 0.1818, 0.1834, 0.3042, 0.5248, 0.4319, 0.2912]

# Emergent average momentum
⟨P_μ⟩ ≈ 0.709

# Simulated effective curvature (discrete)
curvature ≈ [0.9746, 0.9624, 1.0472, 0.3447, -0.7718, -1.2557, -0.5075, 1.0304, 1.0145, -0.4937,
 -1.1522, 0.8359, 1.2701, -0.4039, -0.6445, -0.7903, 0.0176, 0.7667, -0.0750, -0.6218]

4. Extension to Perceptible Dimensions

• For 2D or 3D, each fragment would have coordinates (xi,yi)(x_i, y_i)(xi,yi) or (xi,yi,zi)(x_i, y_i, z_i)(xi,yi,zi)

• The correlation function f(xi,xj)f(x_i, x_j)f(xi,xj) adapts using Euclidean distance in that space

• Emergent curvature generalizes to 2×2 or 3×3 tensors, representing approximate geometry

• At large scales, the reconstructed geometry resembles Einstein’s description, while at small scales, local fluctuations appear due to breaking of supersymmetry

5. Discussion and Open Questions

1. This model is exploratory, but it demonstrates how SUSY can emerge locally and why we do not observe it directly.

2. Emergent gravity appears coherent at large scales even though fragments are asymmetric.

3. Questions for discussion:

   • Are there similar works on local breaking of SUSY?

   • How could this idea extend to quantum fields and real dynamics?

   • What experiments could detect fluctuations from this fragmented supersymmetry?

6. Conclusion

Fragmented supersymmetry offers a new conceptual approach: a universe where SUSY and gravity emerge from imperfect local structures. At large scales, coherence and average symmetry are recovered, while at small scales, fragments generate variations and potentially detectable deviations.

I can share an interactive notebook that allows adjusting ε(x_i), ℓ_c, and other parameters to see how different geometries emerge.