Quantized Nambu-Poisson Manifolds in a 3-Lie Algebra Reduced Model

TL;DR

This paper constructs stable solutions in a reduced 3-Lie algebra model that correspond to quantized Nambu-Poisson manifolds, linking them to noncommutative spaces and effective field theories in string theory contexts.

Contribution

It introduces a zero-dimensional 3-Lie algebra model with stable solutions representing quantized Nambu-Poisson manifolds and connects these to the IKKT matrix model and noncommutative field theories.

Findings

Solutions correspond to noncommutative spaces like S^3, R^3, and Hpp-waves.

Expansion around solutions yields complex noncommutative field theories.

The model relates to a cubic supermatrix model with osp(1|32) supersymmetry.

Abstract

We consider dimensional reduction of the Bagger-Lambert-Gustavsson theory to a zero-dimensional 3-Lie algebra model and construct various stable solutions corresponding to quantized Nambu-Poisson manifolds. A recently proposed Higgs mechanism reduces this model to the IKKT matrix model. We find that in the strong coupling limit, our solutions correspond to ordinary noncommutative spaces arising as stable solutions in the IKKT model with D-brane backgrounds. In particular, this happens for S^3, R^3 and five-dimensional Neveu-Schwarz Hpp-waves. We expand our model around these backgrounds and find effective noncommutative field theories with complicated interactions involving higher-derivative terms. We also describe the relation of our reduced model to a cubic supermatrix model based on an osp(1|32) supersymmetry algebra.