HSQG · Higher Spin Quantum Gravity: Lagrangian Formulations for Higher Spin Gravity and Their Applications

The research proposed here is principally aimed at deriving action for higher-spin (HS) gravity theories, to quartic order in fields, mainly focused in dimensions three, four and five, by using Noether method, adapted to HS systems. We will find out what are the conditions for the action for HS gravity to exist and what spectrum is allowed, what are the locality properties of such theories and what is the role of special dimensions. We will further explicate the role of the cosmological constant and parity odd structures in such theories. In particular, we will study the zoo of five dimensional HS algebras and their role in formulations of different HS gravity theories in five and lower dimensions. The result of this research will be the answer to long-standing questions of existence and uniqueness of action formulation for field theories with massless HS spectrum. The obtained information will have wide applications in Quantum Gravity. In particular, the knowledge of the action to quartic order in fields will allow us to compute the one-loop mass renormalization of HS fields and compare to known results in the conjectured dual CFT, thus providing a non-trivial check for the AdS/CFT conjecture.