2012/03/31 by J. Greitz, P. S. Howe, Paul Howe · 20 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Affine Lie algebra #Algebra over a field #Algebraic number #Algebraic structure #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Current algebra #Duality (order theory) #Geometry #Homogeneous space #Lie algebra #Lie superalgebra #Mathematical analysis #Mathematical physics #Mathematics #Physics #Pure mathematics #Superconformal algebra #Supergravity #Superspace #Supersymmetry #Supersymmetry algebra #hep-th
paper · pdf · doi:10.1007/jhep06(2012)177
published in Journal of High Energy Physics 2012(6) (Springer Nature) · 30 pages. References added. Some clarification of the text
arxiv created 2012/04/28 · openalex publication_date 2012/06/01 · arxiv updated 2015/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The half-maximal supergravity theories in three dimensions, which have local SO(8)\xz SO(n) and rigid SO(8,n) symmetries, are discussed in a superspace setting starting from the superconformal theory. The on-shell theory is obtained by imposing further constraints; it is essentially a non-linear sigma model that induces a Poincaré supergeometry. The deformations of the geometry due to gauging are briefly discussed. The possible p-form field strengths are studied using supersymmetry and SO(8,n) symmetry. The set of such forms obeying consistent Bianchi identities constitutes a Lie super co-algebra while the demand that these identities admit solutions places a further constraint on the possible representations of SO(8,n) that the forms transform under which can be easily understood using superspace cohomology. The dual Lie superalgebra can then be identified as the positive sector of a Borcherds superalgebra that extends the Lie algebra of the duality group. In addition to the known p=2,3,4 forms, which we construct explicitly, there are five-forms that can be non-zero in supergravity, while all forms with p>5 vanish. It is shown that some six-forms can have non-trivial contributions at order \a'.