Holographic duals to Poisson sigma models and noncommutative quantum mechanics

TL;DR

This paper demonstrates that Poisson sigma models on a finite cylinder are equivalent to noncommutative quantum mechanics at the boundary, revealing a deep connection between 2D field theories and quantum mechanics.

Contribution

It establishes a novel equivalence between Poisson sigma models and noncommutative quantum mechanics using Hamiltonian reduction.

Findings

Poisson sigma models can be reduced to boundary noncommutative quantum mechanics

The equivalence holds for well-behaving Poisson tensors on finite cylinders

Provides new insights into the boundary dynamics of 2D theories

Abstract

Poisson sigma models are a very rich class of two-dimensional theories that includes, in particular, all 2D dilaton gravities. By using the Hamiltonian reduction method, we show that a Poisson sigma model (with a sufficiently well-behaving Poisson tensor) on a finite cylinder is equivalent to a noncommutative quantum mechanics for the boundary data.