Off-shell Algebra Research Articles

Gauge theories, duality relations and the tensor hierarchy

We compute the complete 3- and 4-dimensional tensor hierarchies, i.e. sets of p-form fields, with 1 ≤ p ≤ D, which realize an off-shell algebra of bosonic gauge transformations. We show how these tensor hierarchies can be put on-shell by introducing a set of duality relations, thereby introducing additional scalars and a metric tensor. These so-called duality hierarchies encode the equations of motion of the bosonic part of the most general gauged supergravity theories in those dimensions, including the (projected) scalar equations of motion. We construct gauge-invariant actions that include all the fields in the tensor hierarchies. We elucidate the relation between the gauge transformations of the p-form fields in the action and those of the same fields in the tensor hierarchy.

A CANONICAL APPROACH TO THE EINSTEIN–HILBERT ACTION IN TWO SPACETIME DIMENSIONS

The canonical structure of the Einstein–Hilbert Lagrange density [Formula: see text] is examined in two spacetime dimensions, using the metric density [Formula: see text] and symmetric affine connection [Formula: see text] as dynamical variables. The Hamiltonian reduces to a linear combination of three first-class constraints with a local SO (2, 1) algebra. The first-class constraints are used to find a generator of gauge transformations that has a closed off-shell algebra and which leaves the Lagrangian and det (hμν) invariant. These transformations are distinct from diffeomorphism invariance, and are gauge transformations characterized by a symmetric matrix ζμν.

Off-shell no-go theorems for higher dimensional supersymmetries and supergravities

By a simple fermion counting argument we show in which space-time dimensions the existence of off-shell supersymmetric Yang-Mills and supergravity theories with an off-shell supersymmetry algebra without “central charges” are allowed. In particular we show that the maximally extended theories require “central charges” or lose explicit Lorentz covariance (as in the light-cone gauge), and that for N ⩾ 3, d = 4 only N = 4 supergravity coupled to six Yang-Mills multiplets can avoid the theorems and the off-shell algebra may not have “central charges”.