2026/05/31 by Yannick Mvondo-She · 2 citations
Physics and Astronomy · #hep-th
14 pages, title changed, and added new section deriving logarithmic two-point functions from the unified Virasoro flow
arxiv created 2026/08/05 · arxiv updated 2026/08/06
We develop a representation-theoretic framework for the relation between asymptotic symmetry evolution and monodromy in critical topologically massive gravity at the chiral point \(μℓ=1\). We show that continuous evolution generated by the Virasoro zero mode \(L0\) and analytic continuation around branch points are naturally unified as different regimes of a single complex one-parameter flow. At the chiral point, the Virasoro generator becomes non-diagonalizable and admits the Jordan decomposition \( L0=h1+N, \) where \(N\) is nilpotent. We demonstrate that this nilpotent component governs identical mixing structures for both real and imaginary flow parameters, producing linear mixing under continuous evolution and logarithmic mixing under monodromy. The logarithmic sector is therefore characterized by a single indecomposable representation-theoretic structure that is probed uniformly by both transformations. As a direct application of this unified Virasoro flow, we derive the universal functional form of the rank-two logarithmic two-point functions. In this framework, the semisimple part of \(L0\) generates the ordinary conformal power-law scaling, while its nilpotent part generates the logarithmic corrections characteristic of logarithmic conformal field theories. The resulting correlators reproduce the universal logarithmic structure previously obtained from a monodromy analysis~\citeMvondo-She:2026egr, thereby providing an independent derivation and a non-trivial consistency check of the unified-flow formalism. These results establish the unified Virasoro flow not only as a common description of continuous evolution and monodromy, but also as a computational framework for physical observables in the logarithmic sector of critical topologically massive gravity.