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Quantum recovery of target-space Lorentz symmetry in the supermembrane/matrix model

Demonstrate at the quantum level that target-space Lorentz symmetry is recovered in the N → ∞ limit of the maximally supersymmetric SU(N) matrix quantum mechanics (the matrix regularization of the D = 11 supermembrane) by constructing the quantum Lorentz generators and proving their algebra and invariance properties.

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Background

The D = 11 supermembrane admits a matrix regularization in terms of maximally supersymmetric SU(N) matrix quantum mechanics. Classically, target-space Lorentz symmetry is broken at finite N but can be shown to be recovered in the N → ∞ limit via appropriately defined generators.

Extending this recovery to the quantum theory requires a full construction and verification of the Lorentz algebra at the quantum level in the N → ∞ limit, which has remained unresolved.

References

Subsequently it was shown that the supermembrane Hamiltonian, unlike the bosonic membrane Hamiltonian, has a continuous spectrum 75, and, following unpublished work of J. Goldstone, target space Lorentz symmetry generators can be defined for the supersymmetric theory [77] such that classical Lorentz symmetry, which is broken for finite N, is recovered in the N → ∞ limit (the corresponding quantum calculation remains a wide open challenge).

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