DR. SANDIPAN SENGUPTA

In addition to the gravitational (Newton's) constant, gravity theory in four dimensions has three independent topological coupling constants. In the gravity Lagrangian, these show up as coefficients of three topological densities, namely Nieh-Yan, Pontryagin and Euler. We analyse the Hamiltonian theory of gravity based on a generalized Lagrangian containing these three topological densities in addition to the Hilbert-Palatini term. Subsequently, we discuss how the quantum theory of gravity might perceive them within various possible quantization schemes. We also study how the topological parameters affect the gravity action for manifolds with boundaries, and in particular, for asymptotically locally AdS spacetimes. In this case, the Barbero-Immirzi parameter is shown to appear as the only independent topological coupling constant in the action principle. Subsequently, we make a few remarks on the potential implications in the quantum theory of gravity in this context.