Dirac Sigma Models

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.

28 pages, Latex

References in corpus (17)

• Deformation quantization of Poisson manifolds, I
• Two Dimensional Gauge Theories Revisited
• Dilaton Gravity in Two Dimensions
• A path integral approach to the Kontsevich quantization formula
• Two-Dimensional Gravity and Nonlinear Gauge Theory
• Poisson Structure Induced (Topological) Field Theories
• WZW-Poisson manifolds
• Classical and Quantum Gravity in 1+1 Dimensions, Part I: A Unifying Approach
• Current Algebras and Differential Geometry
• Generalized complex manifolds and supersymmetry
• Poisson sigma models and symplectic groupoids
• Lie algebroid morphisms, Poisson Sigma Models, and off-shell closed gauge symmetries
• The Topological G/G WZW Model in the Generalized Momentum Representation
• A sigma model field theoretic realization of Hitchin's generalized complex geometry
• Algebroid Yang-Mills Theories
• Generalized complex geometry and the Poisson Sigma Model
• Quantization of Field Theories Generalizing Gravity-Yang-Mills Systems on the Cylinder

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• Sigma models for genuinely non-geometric backgrounds
• Beyond the standard gauging: gauge symmetries of Dirac Sigma Models
• Nonassociativity, Malcev Algebras and String Theory
• Dirac Sigma Models from Gauging
• 2d Gauge Theories and Generalized Geometry
• Dilaton Gravity, Poisson Sigma Models and Loop Quantum Gravity
• Strings in Singular Space-Times and their Universal Gauge Theory
• p-Brane Actions and Higher Roytenberg Brackets
• Generalized and graded geometry for mechanics: a comprehensive introduction
• Extended generalized geometry and a DBI-type effective action for branes ending on branes
• The BV action of 3D twisted R-Poisson sigma models
• Transverse generalized metrics and 2d sigma models
• On the relation of Lie algebroids to constrained systems and their BV/BFV formulation
• Gauged sigma-models with nonclosed 3-form and twisted Jacobi structures
• The Lie algebroid Poisson sigma model
• Graded geometry in gauge theories and beyond
• Topological Dirac Sigma Models and the Classical Master Equation
• Topological A-Type Models with Flux
• Basic curvature and the Atiyah cocycle in gauge theory
• Dual branes in topological sigma models over Lie groups. BF-theory and non-factorizable Lie bialgebras
• Instances of Higher Geometry in Field Theory