extended supergravity
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| extended supergravity | |
|---|---|
| Name | Extended supergravity |
| Field | Theoretical physics |
| Introduced | 1970s |
| Key people | Bruno de Wit, Daniel Z. Freedman, Sergio Ferrara, Peter van Nieuwenhuizen, John H. Schwarz, Michael B. Green, Edward Witten, Nathan Seiberg, Juan Maldacena, Cumrun Vafa, Andrew Strominger, Shin'ichi Nojiri, Gavin Salam, Paul Townsend, Hugh Osborn, Eric Bergshoeff, Massimo Bianchi, Renata Kallosh, Joseph Polchinski, Leonard Susskind, Gerard 't Hooft, Alessandro Tomasiello, Eugene Cremmer, Bernard Julia, Sergio Ferrara Jr., Stephen Hawking, Steven Weinberg, Lisa Randall, Nima Arkani-Hamed, Howard Georgi, Philip Candelas, Edward Witten Jr., Juan Maldacena Jr., Andrei Linde, Alexei Zamolodchikov, Victor Kac, Peter West, Christoph Keller, Paolo Di Vecchia, Marcus Spradlin, Amir-Kian Kashani-Poor, Thomas Banks, Marta Volonteri, Josephine Johnson, Yukio Okada, Keisuke Arai, Hitoshi Murayama |
extended supergravity Extended supergravity refers to supergravity theories with more than one supersymmetry generator (N>1) that extend local supersymmetry by enlarging the supersymmetry algebra and field content. It sits at the intersection of quantum field theory, string theory, and differential geometry and has been central to developments involving dualities, black hole microphysics, and compactification scenarios. Influential constructions and classifications guided research programs across collaborations at institutions such as CERN, Princeton University, Harvard University, California Institute of Technology, and Institute for Advanced Study.
Introduction
Extended supergravity emerged from efforts by researchers including Daniel Z. Freedman, Peter van Nieuwenhuizen, and Sergio Ferrara to generalize early work in four-dimensional N=1 supersymmetry to theories with extended supersymmetry such as N=2 supersymmetry and N=8 supergravity. These theories were motivated by connections to perturbative and nonperturbative aspects of string theory, proposals like M-theory, and conjectures about ultraviolet behavior of gravity advanced by figures such as Zvi Bern and Lance Dixon. Seminal results tied to names like Eugene Cremmer and Bernard Julia clarified the role of global symmetry groups such as E7(7). Extended supergravity provides a laboratory for testing ideas originating from gatherings at workshops like the Solvay Conference and programs at centers including the Simons Center for Geometry and Physics.
Supersymmetry Algebra and Multiplets
The supersymmetry algebra in extended models enlarges the Poincaré group by multiple supercharges transforming under R-symmetry groups such as SU(8), USp(2N), and U(1). Classification of multiplets—scalar, vector, tensor, and graviton multiplets—was developed in parallel with representation theory research by figures like Victor Kac and Gabriele Veneziano. Higher-N algebras admit central charges linked to extended objects studied in works by Joseph Polchinski and Joseph D. Lykken, while short and long multiplets relate to BPS bounds examined by Andrew Strominger and Cumrun Vafa. Multiplet structure informs anomaly analyses carried out in contexts involving Atiyah–Singer index theorem and collaborations with mathematicians at Institute des Hautes Études Scientifiques.
Construction and Lagrangians
Lagrangian formulations for extended supergravity were constructed using Noether methods, superconformal tensor calculus, and geometric approaches developed by teams including Bruno de Wit and Bernard Julia. Off-shell formulations remain limited for large N, prompting on-shell techniques pioneered in work at Dublin Institute for Advanced Studies and Scuola Normale Superiore. Couplings to matter multiplets and vector multiplet moduli spaces use special geometry introduced by Philip Candelas and expanded by Renata Kallosh. Higher-derivative corrections and loop computations were pursued in collaborations involving Zvi Bern, John H. Schwarz, and Michael B. Green to study quantum consistency and potential ultraviolet cancellations, themes debated at meetings like Strings Conference.
Local Gauging and Supergravity Theories (N>1)
Gauging R-symmetries and nonabelian isometries produces gauged supergravities such as N=8 supergravity and N=4 gauged supergravity, with classification influenced by work from Eugene Cremmer, Bernard Julia, and Bruno de Wit. Freund–Rubin compactifications studied by Peter van Nieuwenhuizen and Paul Townsend relate gauged theories to anti-de Sitter vacua discussed in contexts such as AdS/CFT correspondence by Juan Maldacena. Consistent truncations that link higher-dimensional theories on manifolds like Calabi–Yau manifolds and G2 manifolds to lower-dimensional gauged models were explored by groups at Imperial College London and Max Planck Institute for Physics.
Symmetries, Dualities, and Moduli Spaces
Global symmetry groups in extended supergravity, notably exceptional groups like E7(7), control duality rotations and electromagnetic duality analyzed by Bernard Julia and Boris Pioline. Moduli spaces of scalar fields exhibit special Kähler or quaternionic-Kähler geometry with contributions from mathematicians at Courant Institute and IHÉS. String dualities—S-duality, T-duality, and U-duality—studied by Edward Witten, Cumrun Vafa, and Ashoke Sen map supergravity sectors to brane configurations featured in D-brane literature by Joseph Polchinski. Mirror symmetry connections to Calabi–Yau manifolds and enumerative predictions pursued by Philip Candelas linked moduli-space structure to nonperturbative effects.
Vacua, Compactification, and Spontaneous Supersymmetry Breaking
Vacuum structure and compactifications from eleven-dimensional supergravity and ten-dimensional type II supergravity to four dimensions produce rich landscapes studied by teams at KITP and Perimeter Institute. Mechanisms for spontaneous supersymmetry breaking in extended models involve Scherk–Schwarz reductions associated with work by Joël Scherk and John Schwarz and flux compactifications investigated by Gilles Moore and Michael Douglas. Stabilization of moduli and uplift to de Sitter vacua engaged researchers like Andrei Linde and Sergio Ferrara, with computational techniques developed in collaborations supported by programs at Kavli Institute for Theoretical Physics.
Applications and Phenomenological Implications
Extended supergravity has informed black hole microstate counting via extremal BPS solutions studied by Andrew Strominger and Cumrun Vafa, entropy computations linked to Strominger–Vafa black hole results, and holographic applications arising from AdS/CFT correspondence exploited by Juan Maldacena and Edward Witten. Phenomenological models incorporate extended sectors in studies from CERN searches to cosmological model building by Nima Arkani-Hamed and Lisa Randall; constraints from collider experiments at Large Hadron Collider and observational programs such as Planck mission feed back into model selection. Mathematical tools and duality-inspired techniques developed across institutions including Institute for Advanced Study continue to influence research in quantum gravity and beyond.