Just as noncommutative gauge theories arise from quantizing open strings in a large magnetic field, non-Abelian two-form gauge theories may conceivably be constructed by quantizing open membranes in a large three-form magnetic background. We make some observations that arise in following this strategy, with an emphasis on the relation to the quantization of volume-preserving diffeomorphisms (VPD). In particular, we construct consistent non-Abelian interactions of a two-form in 3+1 dimensions, based on gauge invariance under VPD.

• Received 8 February 2002

DOI:https://doi.org/10.1103/PhysRevD.66.025010