Large chiral diffeomorphisms on Riemann surfaces and W-algebras
- Dipartimento di Fisica dell'Universita di Genova, Via Dodecaneso 33, I-16146 Genova (Italy) and Istituto Nazionale di Fisica Nucleare, INFN, Sezione di Genova via Dodecaneso 33, I-16146 Genova (Italy)
The diffeomorphism action lifted on truncated (chiral) Taylor expansion of a complex scalar field over a Riemann surface is presented in the paper under the name of large diffeomorphisms. After an heuristic approach, we show how a linear truncation in the Taylor expansion can generate an algebra of symmetry characterized by some structure functions. Such a linear truncation is explicitly realized by introducing the notion of Forsyth frame over the Riemann surface with the help of a conformally covariant algebraic differential equation. The large chiral diffeomorphism action is then implemented through a Becchi-Rouet-Stora (BRS) formulation (for a given order of truncation) leading to a more algebraic setup. In this context the ghost fields behave as holomorphically covariant jets. Subsequently, the link with the so-called W-algebras is made explicit once the ghost parameters are turned from jets into tensorial ghost ones. We give a general solution with the help of the structure functions pertaining to all the possible truncations lower or equal to the given order. This provides another contribution to the relationship between Korteweg-de Vries (KdV) flows and W-diffeomorphims.
- OSTI ID:
- 20861057
- Journal Information:
- Journal of Mathematical Physics, Vol. 47, Issue 10; Other Information: DOI: 10.1063/1.2354588; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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