First Class Constrained Systems and Twisting of Courant Algebroids by a Closed 4-form

Apr, 2009
25 pages
  • Published: Sep 23, 2009 by World Scientific
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Abstract: (arXiv)
We show that in analogy to the introduction of Poisson structures twisted by a closed 3-form by Park and Klimcik-Strobl, the study of three dimensional sigma models with Wess-Zumino term leads in a likewise way to twisting of Courant algebroid structures by closed 4-forms H. The presentation is kept pedagogical and accessible to physicists as well as to mathematicians, explaining in detail in particular the interplay of field transformations in a sigma model with the type of geometrical structures induced on a target. In fact, as we also show, even if one does not know the mathematical concept of a Courant algebroid, the study of a rather general class of 3-dimensional sigma models leads one to that notion by itself. Courant algebroids became of relevance for mathematical physics lately from several perspectives - like for example by means of using generalized complex structures in String Theory. One may expect that their twisting by the curvature H of some 3-form Ramond-Ramond gauge field will become of relevance as well.
Note:
  • Published in 'Fundamental Interactions: A Memorial Volume for Wolfgang Kummer,' Editors: Daniel Grumiller, Anton Rebhan and Dimitri Vassilevich, World Scientific, 2010, pp.115-144
  • 25 pages, invited contribution to the Wolfgang Kummer memorial volume
  • dimension: 3
  • dimension: 2
  • sigma model: nonlinear
  • Wess-Zumino term
  • constraint
  • algebra: twist
  • Hamiltonian formalism