Abstract
We generalize the (n+1)-dimensional twisted R-Poisson topological sigma model with flux on a target Poisson manifold to a Lie algebroid. Analyzing the consistency of constraints in the Hamiltonian formalism and the gauge symmetry in the Lagrangian formalism, geometric conditions of the target space to make the topological sigma model consistent are identified. The geometric condition is an universal compatibility condition of a Lie algebroid with a multisymplectic structure. This condition is a generalization of the momentum map theory of a Lie group and is regarded as a generalization of the momentum section condition of the Lie algebroid.
Highlights
Algebroid structures appear as background mathematical structures in physics, such as T-duality in string theory [1,2,3,4,5,6], gauged nonlinear sigma models [7,8,9,10,11,12,13,14], topological sigma models [15,16,17,18], double field theory [19,20,21,22,23,24,25], etc
The Poisson structure is a fundamental structure of the classical mechanics, and a generalization of Lie algebra, which mainly appears as symmetries
We show that the classical action (7) is consistent if the target space geometric data satisfy Equation (24), i.e., the target space is a premultisymplectic manifold with a Lie algebroid action and a bracket-compatible E flux
Summary
Algebroid structures appear as background mathematical structures in physics, such as T-duality in string theory [1,2,3,4,5,6], gauged nonlinear sigma models [7,8,9,10,11,12,13,14], topological sigma models [15,16,17,18], double field theory [19,20,21,22,23,24,25], etc. We consider a new topological sigma model by generalizing the Poisson structure to a Lie algebroid in the twisted R-Poisson sigma model. We show that the total structure is regarded as a higher Dirac structure of a Lie (n + 1) algebroid Another purpose is to generalize the so-called AKSZ sigma models [34,35,36,37] adding the WZ term. In order to consider generalizations to higher dimensions, first we need to clarify background geometric structures of higher dimensional twisted topological sigma models with the WZ term.
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