I will summarise my research interests and recent work, which is mainly related to the problems of field and gravity theories with extended symmetries. Such systems are the higher-spin and coloured gravity theories, theories of non-abelian chiral p-forms or partially-massless fields (satisfactory interacting theories of which are still missing). [please email a.held@imperial.ac.uk for zoom-link]

We study the possibility for a unitary theory of partially-massless (PM) spin-two field interacting with Gravity in arbitrary dimensions. We show that parity invariant interactions respecting general covariance lead to a reconstruction of Conformal Gravity in even dimensions. In this case the unitarity is sacrificed. By relaxing the parity invariance, we find a possibility of a unitary theory in four dimensions, but the parity-odd cubic vertex cannot be written in usual metric variables. We comment on possible approaches that may allow for the formulation of this theory. Finally, by relaxing the general covariance, we show that a non-minimal coupling between massless and PM spin-two fields may lead to an alternative possibility of a unitary theory, that necessarily involves mixed-symmetry fields.

Higher Spin Algebras are (infinite-dimensional) Lie algebras, that underlie a theory with Higher Spin spectrum. In different space-time dimensions Higher Spin algebras have different properties. I will present a review and some new results on Higher Spin algebras in different dimensions.