Exact Lindbladian Dynamics from Conformal Embeddings and Topological Defects in Conformal Field Theory

• URL: http://arxiv.org/abs/2607.08827v1
• Date: Thu, 09 Jul 2026 18:00:03 GMT
• Title: Exact Lindbladian Dynamics from Conformal Embeddings and Topological Defects in Conformal Field Theory
• Abstract summary: We identify intrinsic conformal structures that restore exact solvability in $(1+1)$D conformal field theories.<n>These examples show that intrinsic conformal structures, such as conformal embeddings and modular data, can organize exactly solvable open conformal dynamics.
• Score: 6.93233370050775
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Analyzing the dynamics of physical observables in open quantum many-body systems is a fundamental but highly challenging task that has yielded very few exact results. In this work, we identify intrinsic conformal structures that restore exact solvability in $(1+1)$D conformal field theories. For $N$ Majorana fermions with linear mode jumps, the adjoint Lindbladian is triangular on reduced even Majorana monomials, yielding recursive exact Heisenberg evolution. In Wess-Zumino-Witten models admitting conformal Majorana embeddings, this hierarchy gives exact dynamics of affine-current products realized as Majorana bilinears, including regimes where the Kac-Moody current algebra alone does not close. In diagonal rational conformal field theories, Verlinde topological defect lines furnish jump operators whose primary-sector dynamics is exactly diagonal: topological-charge probabilities are conserved, while intersector coherences dephase at rates fixed by the modular $S$ matrix and nonnegative measurement strengths. These examples show that intrinsic conformal structures, such as conformal embeddings and modular data, can organize exactly solvable open conformal dynamics.

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