Abstract
A classical Ed(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 Ed(d) generalised Lie derivative. Ed(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 Ed(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 Ed(d)-invariant currents.
Highlights
A derivation of the Ed(d)-invariant current algebra from a canonical Poisson structure is in general not possible
One can derive a current algebra associated to paraHermitian exceptional geometry
Many features generalise to p-branes in SL(p + 3) generalised geometries that form building blocks for the Ed(d)-invariant currents
Summary
The difference between these current algebra brackets is a total world-sheet derivative term dσ ∂(. The O(d, d)-covariant way to derive the current algebra is as Dirac brackets [52, 70] for the constraints. As will be important later, the Dirac procedure naturally constructs a Lie bracket (skewsymmetric and satisfying Jacobi identity) but the calculation seems to work only when neglecting total spatial world-sheet derivative terms. For the string one can derive the Dorfman current algebra (1.3) as a Dirac bracket up to such terms. In case of a generalised parallelisable background the FABC can be chosen to be constant This Hamiltonian formulation takes the form of an E-model
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