Hamiltonian Analysis of Doubled 4d Chern-Simons

TL;DR

This paper performs a Hamiltonian analysis of doubled 4d Chern-Simons theory, revealing its Poisson algebra structure and proposing connections to affine Gaudin models and quantum groups, thus advancing understanding of integrable models.

Contribution

It introduces a Hamiltonian framework for doubled 4d Chern-Simons, identifies its Poisson algebra, and links it to affine Gaudin models and extended quantum groups.

Findings

Poisson algebra matches affine Gaudin model with constraints

Two methods for boundary condition analysis: edge modes and constraints

Conjecture of extended quantum groups and generalized Harish-Chandra isomorphism

Abstract

Motivated by a conjecture that doubled four-dimensional Chern-Simons produces new integrable models, we perform its Hamiltonian analysis and find the theory's Poisson algebra. This requires carefully accounting for a set of boundary conditions that identify two gauge fields. Two methods for doing so are given, one of which is based on edge-modes and the other on a recharacterisation of the boundary conditions as constraints. We find that the Poisson algebra is that of an affine Gaudin model subject to a constraint, generalising the Goddard-Kent-Olive construction (from conformal field theory) to the world of integrable models. We also conjecture the existence of extended quantum groups and a generalisation of the affine Harish-Chandra Isomorphism.