Komar charge of N = 2 supergravity and its superspace generalization

Summary

The article discusses the construction of a supersymmetric invariant generalized Komar 2-form for minimal N=2, d=4 supergravity using superspace techniques.

Highlights

• The superspace constraints for minimal N=2 supergravity are obtained from the generalized action.
• The on-shell superspace description of minimal N=2 supergravity is derived.
• A Killing supervector in on-shell superspace is defined.
• The super-Komar form is constructed using the Killing supervector and superfield momentum maps.
• The super-Komar form is shown to be closed on-shell and its lowest component gives a gauge, chiral-duality, and supersymmetry invariant generalized Komar 2-form.
• The superspace construction is compared to the component formalism and shown to be more efficient.
• The generalized Komar 2-form is shown to be invariant under supersymmetry up to a total derivative.

Key Insights

• The superspace approach provides a more efficient method for constructing the generalized Komar 2-form compared to the component formalism.
• The introduction of a magnetic momentum map is necessary to construct the super-Komar form in a duality-invariant manner.
• The super-Komar form's closure on-shell guarantees that its lowest component is a closed spacetime 2-form, which is a desirable property for a generalized Komar 2-form.
• The supersymmetry invariance of the generalized Komar 2-form up to a total derivative is a key feature that distinguishes it from other constructions.
• The construction of the super-Komar form relies on the use of superfield momentum maps, which are associated with the basic superfield gauge symmetries in the on-shell superspace.
• The generalized Komar 2-form has potential applications in supersymmetric black hole thermodynamics, particularly in the study of black holes with fermionic hair.
• The superspace approach can be generalized to other supergravity theories, providing a powerful tool for constructing generalized Komar forms in more complex theories.

Mindmap

Citation

Bandos, I., Meessen, P., & Ortín, T. (2024). Komar charge of N = 2 supergravity and its superspace generalization (Version 1). arXiv. https://doi.org/10.48550/ARXIV.2412.18510