Abstract We investigate the emergence of topological defect lines in the conformal Regge limit of two-dimensional conformal field theory. We explain how a local operator can be factorized into a holomorphic and an anti-holomorphic defect operator connected through a topological defect line, and discuss implications on analyticity and Lorentzian dynamics including aspects of chaos. We derive a formula relating the infinite boost limit, which holographically encodes the “opacity” of bulk scattering, to the action of topological defect lines on local operators. Leveraging the unitary bound on the opacity and the positivity of fusion coefficients, we show that the spectral radii of a large class of topological defect lines are given by their loop expectation values. Factorization also gives a formula relating the local and defect operator algebras and fusion categorical data. We then review factorization in rational conformal field theory from a defect perspective, and examine irrational theories. On the orbifold branch of the c = 1 free boson theory, we find a unified description for the topological defect lines through which the twist fields are factorized; at irrational points, the twist fields factorize through “non-compact” topological defect lines which exhibit continuous defect operator spectra. Along the way, we initiate the development of a formalism to characterize non-compact topological defect lines.
This paper shows that particle-like excitations can emerge naturally within classical wave physics as topological defects of an effective wavefield. Focusing on a two-dimensional elastic medium whose envelope dynamics reduces to an effective Schrödinger equation, we demonstrate that phase singularities—points where the wave amplitude vanishes—behave as robust, localized objects carrying conserved topological charge. These defects follow deterministic trajectories governed by a guidance equation formally identical to that of de Broglie–Bohm pilot-wave theory, yet derived entirely from classical continuum mechanics without invoking quantum postulates. The central result is that defect cores move with velocityv=(ℏeff/meff)∇S,\mathbf{v} = (\hbar_{\mathrm{eff}}/m_{\mathrm{eff}})\nabla S,v=(ℏeff/meff)∇S,where
S is the phase of the emergent wavefunction. This wave-guided dynamics arises as a kinematic constraint: the defect must remain a zero of the evolving field. The paper presents an asymptotic analysis of defect structure and motion, and discusses both the parallels with quantum particle dynamics and the fundamental limitations of the analogy, including the absence of superposed trajectories, entanglement, and quantum statistics. Overall, the work provides a concrete example of how topology and dispersion in classical systems can give rise to quantum-like behavior without quantization, illustrating a physically transparent route to emergent particle dynamics. Keywords: emergent dynamics; topological defects; phase singularities; pilot-wave theory; classical analogs of quantum mechanics; Schrödinger equation; guidance equation; elastic waves
We study nonequilibrium dynamics of relativistic N -component scalar field theories in Minkowski space-time in a classical statistical regime, where typical occupation numbers of modes are much larger than unity. In this strongly correlated system far from equilibrium, the role of different phenomena such as nonlinear wave propagation and defect dynamics remains to be clarified. We employ persistent homology to infer topological features of the nonequilibrium many-body system for different numbers of field components N via a hierarchy of cubical complexes. Specifically, we show that the persistent homology of local energy density fluctuations can give rise to signatures of self-similar scaling associated with topological defects, distinct from the scaling behavior of nonlinear wave modes. This contributes to the systematic understanding of the role of topological defects for far-from-equilibrium time evolutions of nonlinear many-body systems. Published by the American Physical Society 2024