Currents, charges and algebras in exceptional generalised geometry
David Osten
Abstract
A bstract A classical E d ( d ) -invariant Hamiltonian formulation of world-volume theories of half-BPS p -branes in type IIb and eleven-dimensional supergravity is proposed, extending known results to d ≤ 6. It consists of a Hamiltonian, characterised by a generalised metric, and a current algebra constructed s.t. it reproduces the E d ( d ) generalised Lie derivative. E d ( d ) -covariance necessitates the introduction of so-called charges, specifying the type of p -brane and the choice of section. For p > 2, currents of p -branes are generically non- geometric due to the imposition of U -duality, e.g. the M5-currents contain coordinates associated to the M2-momentum. A derivation of the E d ( d ) -invariant current algebra from a canonical Poisson structure is in general not possible. At most, one can derive a current algebra associated to para-Hermitian exceptional geometry. The membrane in the SL(5)-theory is studied in detail. It is shown that in a generalised frame the current algebra is twisted by the generalised fluxes. As a consistency check, the double dimensional reduction from membranes in M-theory to strings in type IIa string theory is performed. Many features generalise to p -branes in SL( p + 3) generalised geometries that form building blocks for the E d ( d ) -invariant currents.