International Research journal of Management Science and Technology
ISSN 2250 - 1959 (online) ISSN 2348 - 9367 (Print) New DOI : 10.32804/IRJMST
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ALGEBRAS AND DIFFERENTIAL GEOMETRY
1 Author(s): RAJ KUMARI
Vol - 11, Issue- 10 , Page(s) : 73 - 85 (2020 ) DOI : https://doi.org/10.32804/IRJMST
We show that symmetries and gauge symmetries of a large class of 2-dimensional σ-models are described by a new type of a current algebra. The currents are labeled by pairs of a vector field and a 1-form on the target space of the σ-model. We compute the current-current commutator and analyse the anomaly cancellation condition, which can be interpreted geometrically in terms of Dirac structures, previously studied in the mathematical literature. Generalized complex structures correspond to decomposi- tions of the current algebra into pairs of anomaly free subalgebras. σ-models that we can treat with our method include both physical and topological examples, with and without Wess-Zumino type terms.