Beyond the standard gauging: gauge symmetries of Dirac Sigma Models

Abstract

In this paper we study the general conditions that have to be met for a gauged extension of a two-dimensional bosonic sigma-model to exist. In an inversion of the usual approach of identifying a global symmetry and then promoting it to a local one, we focus directly on the gauge symmetries of the theory. This allows for action functionals which are gauge invariant for rather general background fields in the sense that their invariance conditions are milder than the usual case. In particular, the vector fields that control the gauging need not be Killing. The relaxation of isometry for the background fields is controlled by two connections on a Lie algebroid L in which the gauge fields take values, in a generalization of the common Lie-algebraic picture. Here we show that these connections can always be determined when L is a Dirac structure in the H-twisted Courant algebroid. This also leads us to a derivation of the general form for the gauge symmetries of a wide class of two-dimensional topological field theories called Dirac sigma-models, which interpolate between the G/G Wess-Zumino-Witten model and the (Wess-Zumino-term twisted) Poisson sigma model.

arXiv comment1+27 pages; version 2: minor correction in the introduction; version 3: minor corrections to match published version, references updated, acknowledgement added

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• Momentum sections in Hamiltonian mechanics and sigma models
• Transverse generalized metrics and 2d sigma models
• Hidden isometry of "T-duality without isometry"
• Gauged sigma-models with nonclosed 3-form and twisted Jacobi structures
• Homotopy momentum sections on multisymplectic manifolds
• Lie Algebroid Gauging of Non-linear Sigma Models
• Topological Dirac Sigma Models and the Classical Master Equation
• Pre-NQ Manifolds and Correspondence Spaces: the Nilmanifold Example
• Higher dimensional Lie algebroid sigma model with WZ term