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This lagrangian has already been used in the literature to obtain various results: notably the partial breaking of supersymmetry and various extremal black--hole solutions. My emphasis, however, is only on providing the reader with a completely explicit and ready to use component expression of the supergravity action. All the details of the derivation are omitted but all the definitions of the items entering the lagrangian and the supersymmetry transformation rules are given.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"The Complete Form of N=2 Supergravity and its Place in the General Framework of D=4 N--Extended Supergravities","attachmentId":84830873,"attachmentType":"pdf","work_url":"https://www.academia.edu/77518141/The_Complete_Form_of_N_2_Supergravity_and_its_Place_in_the_General_Framework_of_D_4_N_Extended_Supergravities","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" 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ds2-5-body-xs">Journal of High Energy Physics, 2009</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Different representations for the action principle in 4D 𝒩 = 2 supergravity","attachmentId":45785645,"attachmentType":"pdf","work_url":"https://www.academia.edu/25469615/Different_representations_for_the_action_principle_in_4D_N_2_supergravity","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/25469615/Different_representations_for_the_action_principle_in_4D_N_2_supergravity"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="7" data-entity-id="25469611" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/25469611/New_higher_derivative_couplings_in_4D_mathcal_N_2_supergravity">New higher-derivative couplings in 4D $ \mathcal{N} = 2 $ supergravity</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="48979249" href="https://independent.academia.edu/SergeiKuzenko">Sergei Kuzenko</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of High Energy Physics, 2011</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"New higher-derivative couplings in 4D $ \\mathcal{N} = 2 $ supergravity","attachmentId":45785656,"attachmentType":"pdf","work_url":"https://www.academia.edu/25469611/New_higher_derivative_couplings_in_4D_mathcal_N_2_supergravity","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/25469611/New_higher_derivative_couplings_in_4D_mathcal_N_2_supergravity"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="33281202" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/33281202/D_4_N_1_supergravity_in_superspace_general_overview_and_technical_analysis">D = 4, N = 1 supergravity in superspace: general overview and technical analysis</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="9338513" href="https://talentgate.academia.edu/PaoloDiSia">Paolo Di Sia</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2018</p><p class="ds-related-work--abstract ds2-5-body-sm">Considering the supersymmetry, the Einstein theory of general relativity brings to supergravity and the superspace gives a geometrical meaning to the supersymmetry transformations. I consider in this work the technical complete construction of D = 4, N = 1 supergravity in a geometrical way, i.e. using superforms in superspace as extension of spinortensor calculus. Starting by the pure D = 4, N = 1 supergravity, the coupling with scalar multiplets (multiplets of Wess-Zumino) and vector multiplets is performed. I use the concepts of supersymmetry, superspace and rheonomic principle. Bianchi identities are analyzed and resolved, ending with the Bianchi identity of gravitino. Supergravity theories are the effective theories of superstring theories.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"D = 4, N = 1 supergravity in superspace: general overview and technical analysis","attachmentId":55751646,"attachmentType":"pdf","work_url":"https://www.academia.edu/33281202/D_4_N_1_supergravity_in_superspace_general_overview_and_technical_analysis","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/33281202/D_4_N_1_supergravity_in_superspace_general_overview_and_technical_analysis"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="15268821" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/15268821/Su_4_invariant_supergravity_theory">Su(4) invariant supergravity theory</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="34346070" href="https://independent.academia.edu/SergioFerrara1">Sergio Ferrara</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Physics Letters B, 1978</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Su(4) invariant supergravity theory","attachmentId":43381986,"attachmentType":"pdf","work_url":"https://www.academia.edu/15268821/Su_4_invariant_supergravity_theory","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/15268821/Su_4_invariant_supergravity_theory"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":42137319,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":42137319,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_42137319" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. 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data-author-id="59551295" href="https://tmu-jp.academia.edu/SergeiKetov">Sergei Ketov</a></div><p class="ds-related-work--metadata ds2-5-body-xs">1996</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"ITP – UH – 15 / 96 revised version ( 4 , 4 ) SUPERFIELD SUPERGRAVITY 1","attachmentId":80329048,"attachmentType":"pdf","work_url":"https://www.academia.edu/70679394/ITP_UH_15_96_revised_version_4_4_SUPERFIELD_SUPERGRAVITY_1","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/70679394/ITP_UH_15_96_revised_version_4_4_SUPERFIELD_SUPERGRAVITY_1"><span class="ds2-5-text-link__content">View 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class="ds-related-work--metadata ds2-5-body-xs">Journal of High Energy Physics</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Higher derivative invariants in four dimensional 𝒩 = 3 Poincaré supergravity","attachmentId":109308520,"attachmentType":"pdf","work_url":"https://www.academia.edu/111915469/Higher_derivative_invariants_in_four_dimensional_N_3_Poincar%C3%A9_supergravity","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/111915469/Higher_derivative_invariants_in_four_dimensional_N_3_Poincar%C3%A9_supergravity"><span class="ds2-5-text-link__content">View PDF</span><span 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href="https://www.academia.edu/4982490/Supergravity_in_2_1_dimensionsfrom_3_1_dimensional_supergravity">Supergravity in (2 + 1) dimensionsfrom (3 + 1)-dimensional supergravity</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="6585914" href="https://duoc.academia.edu/patriciosalgado">patricio salgado</a></div><p class="ds-related-work--metadata ds2-5-body-xs">European Physical Journal C, 2004</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Supergravity in (2 + 1) dimensionsfrom (3 + 1)-dimensional supergravity","attachmentId":49500995,"attachmentType":"pdf","work_url":"https://www.academia.edu/4982490/Supergravity_in_2_1_dimensionsfrom_3_1_dimensional_supergravity","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" 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href="https://www.academia.edu/18513999/On_the_formulation_of_D_11_supergravity_and_the_composite_nature_of_its_three_form_gauge_field">On the formulation of D=11 supergravity and the composite nature of its three-form gauge field</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="38544639" href="https://independent.academia.edu/IgorBandos">Igor Bandos</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Annals of Physics, 2005</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On the formulation of D=11 supergravity and the composite nature of its three-form gauge 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of D = 5 supergravity</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="33532086" href="https://polito.academia.edu/RDAuria">R. D'Auria</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Annals of Physics, 1982</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"A new group theoretical technique for the analysis of Bianchi identities and its application to the auxiliary field problem of D = 5 supergravity","attachmentId":48931908,"attachmentType":"pdf","work_url":"https://www.academia.edu/28572269/A_new_group_theoretical_technique_for_the_analysis_of_Bianchi_identities_and_its_application_to_the_auxiliary_field_problem_of_D_5_supergravity","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" 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