Matterdependent Wgravity anomalies of nonlinearly realised symmetries
Abstract
The anomalies of W_{3} gravity are calculated and analysed. There are conventional anomalies depending only on the gauge fields that are proportional to the central charges of the algebra and which cancel against ghost contributions in the critical dimension. In addition, there are anomalies that depend on the matter fields of the theory, some of which are nontrivial and cannot be cancelled. Thus quantum W_{3} gravity with gauge fields of spins two and three is anomalous, but a theory in which all matterdependent anomalies can be cancelled is obtained by adding an infinite number of extra gauge fields. Matterdependent anomalies occur generally for nonlinearly realised symmetries and correspond to quantum modifications of the classical current algebra. For models in which the quantum current algebra closes, such anomalies can be cancelled by modifying the transformations of the fields. If the quantum current algebra does not close (as for W_{3}), then there are matterdependent anomalies that cannot be cancelled.
 Publication:

Physics Letters B
 Pub Date:
 August 1991
 DOI:
 10.1016/03702693(91)90064W
 Bibcode:
 1991PhLB..265..347H