Quantum field theoretic representation of Wilson surfaces: II higher topological coadjoint orbit model

TL;DR

This paper develops a higher-dimensional topological quantum model for Wilson surfaces within higher gauge theory, extending the geometric and Hamiltonian frameworks to establish a partition function realization and analyze its symmetries and invariances.

Contribution

It introduces a 2-dimensional higher gauge theory model for Wilson surfaces, generalizing the coadjoint orbit approach and connecting it to the derived geometric framework and Hamiltonian formalism.

Findings

Model underpins Wilson surface partition functions.

Homotopy invariance for flat higher gauge fields is demonstrated.

The model's relation to derived Kirillov-Kostant-Souriau theory is established.

Abstract

This is the second of a series of two papers devoted to the partition function realization of Wilson surfaces in strict higher gauge theory. A higher 2--dimensional counterpart of the topological coadjoint orbit quantum mechanical model computing Wilson lines is presented based on the derived geometric framework, which has shown its usefulness in 4--dimensional higher Chern--Simons theory. Its symmetries are described. Its quantization is analyzed in the functional integral framework. Strong evidence is provided that the model does indeed underlie the partition function realization of Wilson surfaces. The emergence of the vanishing fake curvature condition is explained and homotopy invariance for a flat higher gauge field is shown. The model's Hamiltonian formulation is further furnished highlighting the model's close relationship to the derived Kirillov-Kostant-Souriau theory developed in the companion paper.