Bulk Monodromy of Logarithmic Graviton Descendants in Critical Topologically Massive Gravity

Abstract

We study the bulk analytic structure of the logarithmic graviton and its global descendants in critical topologically massive gravity. Starting from the Grumiller--Johansson mode, we complexify the radial coordinate and derive its monodromy directly from the branch structure and winding data of the logarithmic radial factor. We then construct the global logarithmic descendants by explicit differential action and show that each descendant decomposes into a universal logarithmic contribution and a log-free meromorphic remainder. This implies a universal unipotent monodromy throughout the global descendant space. The associated nilpotent operator, obtained directly from the bulk analytic continuation, is shown to intertwine the full global $SL(2,\mathbb{R}{)}_L\times SL(2,\mathbb{R}{)}_R$ action. These results provide a direct bulk analytic realization of the logarithmic structure, linking radial monodromy and global conformal symmetry.

30 pages. Title changed. Substantially expanded and revised with new sections on global descendant constructions, complex radial winding numbers, and full $SL(2,\mathbb{R}{)}_L\times SL(2,\mathbb{R}{)}_R$ global conformal algebra compatibility