Introduces Hamiltonian Lie algebroids over Dirac structures as a generalization and applies them to construct gauged Poisson and Dirac sigma models.
Dirac Sigma Models
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abstract
We introduce a new topological sigma model, whose fields are bundle maps from the tangent bundle of a 2-dimensional world-sheet to a Dirac subbundle of an exact Courant algebroid over a target manifold. It generalizes simultaneously the (twisted) Poisson sigma model as well as the G/G-WZW model. The equations of motion are satisfied, iff the corresponding classical field is a Lie algebroid morphism. The Dirac Sigma Model has an inherently topological part as well as a kinetic term which uses a metric on worldsheet and target. The latter contribution serves as a kind of regulator for the theory, while at least classically the gauge invariant content turns out to be independent of any additional structure. In the (twisted) Poisson case one may drop the kinetic term altogether, obtaining the WZ-Poisson sigma model; in general, however, it is compulsory for establishing the morphism property.
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Hamilton Lie algebroids over Dirac structures and sigma models
Introduces Hamiltonian Lie algebroids over Dirac structures as a generalization and applies them to construct gauged Poisson and Dirac sigma models.
- Gauged Courant sigma models