nLab Poisson holography

Idea

A version of the holographic principle relating particle-mechanics controlled by Poisson manifold-phase spaces to 2d Chern-Simons theory in the form of the Poisson sigma-model 2d field theory.

See the discussion and references here:

• holographic principle – Poisson holography

  • off-shell Poisson bracket – boundary field theory interpretation

  • motivic quantization – The Poisson manifold at the boundary of 2d Poisson-Chern-Simons theory

Further literature

• Joost Nuiten, Sec. 5.2.2 in: Cohomological quantization of local prequantum boundary field theory (August 2013)

which is one of a couple of running examples in

• Quantization via Linear homotopy types

Alternative discussion via factorization algebras:

• Eugene Rabinovich, A Classical Bulk-Boundary Correspondence [arXiv:2202.12332]