The higher-algebraic skeleton of the superstring -- a case study

Abstract

A novel Lie-superalgebraic description of the superstring in the super-Minkowskian background is extracted from the Cartan-Eilenberg super-1-gerbe geometrising the higher gauge field (the Green-Schwarz super-3-cocycle) that couples to the supercharge carried by the superstring. The description assumes the form of a hierarchy of Lie superalgebras integrable to a hierarchy of Lie supergroups and provides a manifestly supersymmetric model of a family of supermanifolds defining a trivialisation of the super-1-gerbe over the embedded superstring worldsheet. The trivialisation, obtained in a purely topological formulation of the superstring dynamics dual to the standard Nambu-Goto-type one, conforms with the gerbe-theoretic representation of extended sources of higher gauge fields known from previous studies of the $\sigma$-model of the bosonic string.

arXiv comment55 pages

References in corpus (21)

• Dirichlet-Branes and Ramond-Ramond Charges
• Introduction to sh Lie algebras for physicists
• Covariant Action for the Super-Five-Brane of M-Theory
• Generating Lie and gauge free differential (super)algebras by expanding Maurer-Cartan forms and Chern-Simons supergravity
• WZW branes and gerbes
• The geometry of branes and extended superspaces
• Geometry of Deligne cohomology
• Super p-Brane Theories and New Spacetime Superalgebras
• The construction of brane and superbrane actions using non-linear realisations
• Pure Spinor Formalism for Osp(N|4) backgrounds
• Bi-branes: Target Space Geometry for World Sheet topological Defects
• Automorphisms, Non-linear Realizations and Branes
• Abelian and non-Abelian branes in WZW models and gerbes
• Basic gerbe over non simply connected compact groups
• Constructions with bundle gerbes
• Kappa-Symmetry of Green-Schwarz Actions in Coset Superspaces
• Division Algebras, Supersymmetry and Higher Gauge Theory
• The gauging of two-dimensional bosonic sigma models on world-sheets with defects
• p-brane superalgebras via integrability
• Bundle gerbes on supermanifolds
• Deriving all p-brane superalgebras via integrability