Creation operators for 2-branes and duality in BF and Chern-Simons theories in D=5

TL;DR

This paper constructs creation operators for 2-branes and topological excitations in 5D BF and Chern-Simons theories, revealing dualities and fermionic statistics, advancing the understanding of quantum membrane quantization.

Contribution

It explicitly constructs creation operators for 2-branes and topological charges in 5D BF and Chern-Simons theories, and explores duality and statistics of these excitations.

Findings

Operators create membrane and topological charge states.

Duality relates membrane and excitation operators.

Membranes can exhibit fermionic statistics.

Abstract

We explicitly construct the creation operators for the quantum field configurations associated to quantum membranes (2-branes) in BF and generalized Chern-Simons theories in a spacetime of dimension D=5. The creation operators for quantum excitations carrying topological charge are also obtained in the same theories. For the case of D=5 generalized Chern-Simons theory, we show that this operator actually creates an open string with a topological charge at its tip. It is shown that a duality structure exists in general, relating the membrane and topological excitation operators and the corresponding dual algebra is derived. Composite topologically charged membranes are shown to possess generalized statistics that may, in particular, be fermionic. This is the first step for the bosonization procedure in these theories. Potential applications in the full quantization of 2-branes is also briefly discussed.