2022/10/31 by Sergei M. Kuzenko, Kuzenko, S. M., E. S. N. Raptakis +3
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.2210.17088
openalex publication_date 2022/10/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The superspace formalism for N=1 supergravity in four dimensions is a powerful geometric setting to engineer off-shell supergravity-matter theories, including higher-derivative couplings. This review provides a unified description of the three superspace approaches to N=1 conformal supergravity: (i) conformal superspace; (ii) U(1) superspace; and (iii) the Grimm-Wess-Zumino formalism. The prepotential formulation for the latter is discussed. We briefly describe the known off-shell formulations for Poincaré and anti-de Sitter supergravity theories as conformal supergravity coupled to certain compensators. As simple applications of the formalism, we present the superfield equations of motion for various off-shell formulations for pure Poincaré and anti-de Sitter supergravity, and show that every solution of these equations is also a solution of the equations of motion for conformal supergravity.