Virasoro Zero-Mode Flow in Critical Topologically Massive Gravity: Logarithmic Correlators and Partition Function Grading

We study the rank-two logarithmic sector of critical Topologically Massive Gravity through the Virasoro zero-mode action \[ U(s,\bar s)=e^{-sL_0-\bar s\bar L_0}. \] Writing $L_0=h\mathbf 1+\frac{1}{2}N$ and $\bar L_0=\bar h\mathbf 1+\frac{1}{2}N$, with $N^2=0$, separates the semisimple conformal g