2004/10/31 by Anton Alekseev, Thomas Strobl · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Current (fluid) #Current algebra #Differential (mechanical device) #Differential geometry #Geometry #Homotopy and Cohomology in Algebraic Topology #Mathematics #Physics #Pure mathematics #hep-th #math-ph #math.DG #math.MP
paper · pdf · doi:10.1088/1126-6708/2005/03/035
published as JHEP 0503 (2005) 035 · 14 pages. Dedicated to Ludwig Faddeev on the occasion of his 70th birthday. References and a new paragraph added
openalex publication_date 2005/03/15 · arxiv created 2005/03/20 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We show that symmetries and gauge symmetries of a large class of 2-dimensional sigma 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 sigma 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 decompositions of the current algebra into pairs of anomaly free subalgebras. Sigma models that we can treat with our method include both physical and topological examples, with and without Wess-Zumino type terms.