Currents, charges and algebras in exceptional generalised geometry

<jats:title>A<jats:sc>bstract</jats:sc> </jats:title><jats:p>A classical <jats:italic>E</jats:italic><jats:sub><jats:italic>d</jats:italic>(<jats:italic>d</jats:italic>)</jats:sub>-invariant Hamiltonian formulation of world-volume theories of half-BPS <jats:italic>p</jats:italic>-branes in type IIb and eleven-dimensional supergravity is proposed, extending known results to <jats:italic>d</jats:italic> ≤ 6. It consists of a Hamiltonian, characterised by a generalised metric, and a current algebra constructed s.t. it reproduces the <jats:italic>E</jats:italic><jats:sub><jats:italic>d</jats:italic>(<jats:italic>d</jats:italic>)</jats:sub> generalised Lie derivative. <jats:italic>E</jats:italic><jats:sub><jats:italic>d</jats:italic>(<jats:italic>d</jats:italic>)</jats:sub>-covariance necessitates the introduction of so-called charges, specifying the type of <jats:italic>p</jats:italic>-brane and the choice of section. For <jats:italic>p ></jats:italic> 2, currents of <jats:italic>p</jats:italic>-branes are generically non- geometric due to the imposition of <jats:italic>U</jats:italic>-duality, e.g. the M5-currents contain coordinates associated to the M2-momentum.</jats:p><jats:p>A derivation of the <jats:italic>E</jats:italic><jats:sub><jats:italic>d</jats:italic>(<jats:italic>d</jats:italic>)</jats:sub>-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.</jats:p><jats:p>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 <jats:italic>p</jats:italic>-branes in SL(<jats:italic>p</jats:italic> + 3) generalised geometries that form building blocks for the <jats:italic>E</jats:italic><jats:sub><jats:italic>d</jats:italic>(<jats:italic>d</jats:italic>)</jats:sub>-invariant currents.</jats:p>