On the Sugawara Current Algebra Proposal for M-Theory

We examine the proposal of [29] that M-theory may admit a Sugawara-type current algebra formulation based on [Formula: see text] [Formula: see text] [Formula: see text]. Motivated by the role of generalized coordinates in E-theory, we ask whether current algebra relations of this type can be derived in a setting that includes those coordinates systematically. We show that such a construction can indeed be carried out for a rigid [Formula: see text] model in which the generalized coordinates are treated as inert under the rigid symmetry, in contrast with E-theory. We also argue that the bilinear form entering the Schwinger term requires closer scrutiny, since any natural ad-invariant extension of the [Formula: see text] Cartan-Killing form to [Formula: see text] [Formula: see text] [Formula: see text] is degenerate.