MEMBRANE SYMMETRIES AND ANOMALIES

The symmetries of the bosonic membrane are analysed in several gauges. We discuss two Lorentz-covariant gauges, and a new light-cone gauge that reduces the membrane hamiltonian to a quadratic form which is diagonalized by harmonic oscillators. We then discuss in detail the Lorentz-covariant quantization and the algebra of constraints that corresponds to the diffeomorphisms in three dimensions (Diff V3). We introduce an operator product expansion which allows the careful computation of commutators. We find that the subalgebras corresponding to diffeomorphisms of the two-dimensional genus-g membrane surface (Diff Σg) and the area-preserving diffeomorphisms (AP Diff Σg) do not have any anomalies, but the full algebra DiffV3 has operator anomalies which render the quantization inconsistent. We thus conclude that purely bosonic membranes are quantum mechanically inconsistent in any number of dimensions d. © 1990.