Courant algebroid relations define spinor and Dirac structure relations, with T-duality inducing spinor relations that generalize twisted cohomology isomorphisms and are compatible with Type II supergravity equations.
On the structure of graded symplectic supermanifolds and Courant algebroids
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abstract
This paper is devoted to a study of geometric structures expressible in terms of graded symplectic supermanifolds. We extend the classical BRST formalism to arbitrary pseudo-Euclidean vector bundles (E\to M_{0}) by canonically associating to such a bundle a graded symplectic supermanifold ((M,\Omega)), with (\textrm{deg}(\Omega)=2). Conversely, every such manifold arises in this way. We describe the algebra of functions on (M) in terms of (E) and show that ``BRST charges'' on (M) correspond to Courant algebroid structures on (E), thereby constructing the standard complex for the latter as a generalization of the classical BRST complex. As an application of these ideas, we prove the acyclicity of ``higher de Rham complexes'', a generalization of a classic result of Fr\"{o}hlicher-Nijenhuis, and derive several easy but useful corollaries.
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2026 2verdicts
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Reviews homotopies in geometric BV formalism and builds new examples from RG flow and gauge changes to produce spans of quantum master actions with isomorphic effective actions.
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Generalised Complex and Spinor Relations
Courant algebroid relations define spinor and Dirac structure relations, with T-duality inducing spinor relations that generalize twisted cohomology isomorphisms and are compatible with Type II supergravity equations.
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Homotopies in Batalin-Vilkovisky Formalism
Reviews homotopies in geometric BV formalism and builds new examples from RG flow and gauge changes to produce spans of quantum master actions with isomorphic effective actions.