The coupling of scalars fields to chiral W3 gravity is reviewed. In general the quantum current algebra generated by the spin-two and three currents does not close when the "natural" regularization (corresponding to the normal ordering with respect to the modes of ∂ϕi) is used, and the non-closure reflects matter-dependent anomalies in the path integral quantization. We consider the most general modification of the current, involving higher derivative "background charge" terms, and find the conditions for them to form a closed algebra in the "natural" regularization. These conditions can be satisfied only for the two-boson model. In that case, it is possible to cancel all the matter-dependent anomalies by adding finite local counter terms to the action and modifying the transformation rules of the fields.
Many W -algebras (e.g. the W N algebras) are consistent for all values of the central charge except for a discrete set of exceptional values. We show that such algebras can be contracted to new consistent degenerate algebras at these exceptional values of the central charge.
The conventional quantization of w 3 strings gives theories which are equivalent to special cases of bosonic strings. We explore whether a more general quantization can lead to new generalized W 3 string theories by seeking to construct quantum BRST charges directly without requiring the existence of a quantum W 3 algebra. We study W 3 -like strings with a direct spacetime interpretationthat is, with matter given by explicit free field realizations. Special emphasis is placed on the attempt to construct a quantum W-string associated with the magic realizations of the classical w 3 algebra. We give the general conditions for the existence of W 3 -like strings, and comment how the known results fit into our general construction. Our results are negative: we find no new consistent string theories, and in particular rule out the possibility of critical strings based on the magic realizations.
This is a synthetic presentation of several barrelledness notions, in locally convex algebras. These are characterized, as in locally convex spaces, via (algebra) seminorms. This approach reveals a new notion of barrelledness. The latter shows to be what is needed to have meaningful statements in locally uniformly convex algebras.
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