Half-maximal supergravity in three dimensions: supergeometry, differential forms and algebraic structure

Abstract

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 $\a'$.

30 pages. References added. Some clarification of the text

References in corpus (6)

• ICTP Lectures on Covariant Quantization of the Superstring
• The E_{11} origin of all maximal supergravities
• Kac-Moody Spectrum of (Half-)Maximal Supergravities
• Gauged Supergravities in Various Spacetime Dimensions
• Maximal supergravity in three dimensions: supergeometry and differential forms
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Cited by in corpus (12)

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• Four-derivative couplings and BPS dyons in heterotic CHL orbifolds
• Exact effective interactions and 1/4-BPS dyons in heterotic CHL orbifolds
• Oxidizing Borcherds symmetries
• All Chern-Simons Invariants of 4D, N = 1 Gauged Superform Hierarchies
• Notophs of N = 8 supergravity
• Borcherds and Kac-Moody extensions of simple finite-dimensional Lie algebras