Aspects des théories de spin élevé avec fermions

The present thesis is divided into three parts. In Part I we address a problem within Higher-Spin Gauge Theory in dimension three: namely, that of computing the asymptotic symmetry algebra of supersymmetric models, describing an infinite spectrum of integer and half-integer higher-spin fields. In Part II we investigate higher-spin theories in dimension four or greater, where we classify the consistent cross interactions between free gauge fermions of arbitrary spin and a photon or a graviton. A third part supplements the bulk of the manuscript with technical appendices. <p><p>Part I is concerned with the Higher-Spin Theory extending the anti-de Sitter orthosymplectic Supergravity in three dimensions. After recalling the construction of the latter we exhibit the structure of the former, and then explain how to generalize the boundary conditions for Supergravity to the higher-spin case. Following the usual procedure, we compute the form of the residual gauge parameter and then identify the Poisson-bracket algebra governing the asymptotic dynamics. It is found to be a nonlinear, supersymmetric algebra of the W-infinity type with same central charge as pure Gravity in the Virasoro sector, which is a subalgebra thereof. The simply supersymmetric case is treated explicitly whereas the details of the extended cases are relegated to the appendices. <p><p>Part II deals with the interaction problem for gauge fermions coupled to Electromagnetism and Gravity in flat spacetime of arbitrary dimension. First we recall the so-called BRST-Antifield techniques, which reformulate the deformation problem as a cohomological one, recasting the familiar Noether procedure for finding out interactions in a mathematically systematic way. We then use these methods to classify and obtain expressions for the gauge-invariant cubic couplings between a symmetric tensor-spinor and a spin-1 and spin-2 gauge field. With no input from previous works, we find the complete list of interaction terms with minimal assumptions and in particular shed light on the quartic obstructions to full consistency.Doctorat en Sciences