Aspects of three-dimensional higher-curvature gravities

Understand

We present new results involving general higher-curvature gravities in three dimensions.

• The most general Lagrangian can be written as a function of the Ricci scalar $R$, $\mathcal{S}_2\equiv \tilde R_{a}^b \tilde R_b^a$ and $\mathcal{S}_3\equiv \tilde R_a^b \tilde R_b^c \tilde R_c^a$ where $\tilde R_{ab}$ is the traceless part of the Ricci tensor.
• First, we provide a formula for the exact number of independent order-$n$ densities, $\#(n)$.
• This satisfies the identity $\#(n-6)=\#(n)-n$.