Abstract
We investigate the asymptotic structure of the free Rarita-Schwinger theory in four spacetime dimensions at spatial infinity in the Hamiltonian formalism. We impose boundary conditions for the spin-3/2 field that are invariant under an infinite-dimensional (abelian) algebra of non-trivial asymptotic fermionic symmetries. The compatibility of this set of boundary conditions with the invariance of the theory under Lorentz boosts requires the introduction of boundary degrees of freedom in the Hamiltonian action, along the lines of electromagnetism. These boundary degrees of freedom modify the symplectic structure by a surface contribution appearing in addition to the standard bulk piece. The Poincaré transformations have then well-defined (integrable, finite) canonical generators. Moreover, improper fermionic gauge symmetries, which are also well-defined canonical transformations, are further enlarged and turn out to be parametrized by two independent angle-dependent spinor functions at infinity, which lead to an infinite-dimensional fermionic algebra endowed with a central charge. We extend next the analysis to the supersymmetric spin-(1, 3/2) and spin-(2, 3/2) multiplets. First, we present the canonical realization of the super-Poincaré algebra on the spin-(1, 3/2) multiplet, which is shown to be consistently enhanced by the infinite-dimensional abelian algebra of angle-dependent bosonic and fermionic improper gauge symmetries associated with the electromagnetic and the Rarita-Schwinger fields, respectively. A similar analysis of the spin-(2, 3/2) multiplet is then carried out to obtain the canonical realization of the super-Poincaré algebra, consistently enhanced by the abelian improper bosonic gauge transformations of the spin-2 field (BMS supertranslations) and the abelian improper fermionic gauge transformations of the spin-3/2 field.
Highlights
Was observed was four-dimensional Einstein gravity with vanishing cosmological constant, where studies at null infinity revealed that the asymptotic symmetries formed the infinitedimensional Bondi-van der Burg-Metzner-Sachs (BMS) algebra [2,3,4,5,6,7,8], which can even be further extended to include super-rotations [9,10,11,12]
We investigate the asymptotic structure of the free Rarita-Schwinger theory in four spacetime dimensions at spatial infinity in the Hamiltonian formalism
We present the canonical realization of the super-Poincaré algebra on the spin-(1, 3/2) multiplet, which is shown to be consistently enhanced by the infinite-dimensional abelian algebra of angle-dependent bosonic and fermionic improper gauge symmetries associated with the electromagnetic and the Rarita-Schwinger fields, respectively
Summary
The less restrictive boundary conditions developed in this paper allow for a O(r−1) term in the gravitino field ψk. One might argue at this point that because the new term ∂kχ in the asymptotic behaviour of ψk is a gradient, it should be irrelevant since it takes the form of a gauge transformation. A similar extension of the boundary conditions by an improper gauge term that is the leading term in the asymptotic expansion of the field was considered earlier in [46]. Anticipating what we shall find below, we already impose the needed extra condition, which expresses that the constraint function S should decay one power of r−1 faster than what generically follows from the boundary conditions on the fields, i.e., it should decay as r−4. The new asymptotic conditions on the gravitino field are checked to be preserved under Poincaré transformations, which we take to coincide with (2.13), δξ ψp. These transformations involve both proper and improper gauge symmetries
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