Landau-Ginzburg Paradigm of Topological Orders and a CFT Factory

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• Yu Zhao (Fudan University)
• Tuesday 02 September 2025, 10:00-11:30
• Seminar Room 2, Newton Institute.

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BID - Quantum field theory with boundaries, impurities, and defects

Topologically ordered phases of matter have long been regarded as lying beyond the Landau–Ginzburg paradigm of symmetry breaking. Our recent studies of anyon condensation, however, suggest that such phases may, in fact, be brought back within the Landau–Ginzburg framework. In this talk, I will present a framework that brings 2+1D topological phases back into the Landau–Ginzburg picture by reformulating the string-net model to be a genuine lattice gauge theory coupled to anyonic matter fields. Within this modified model, topological phase transitions induced by anyon condensation and their consequent phenomena, such as order parameter fields, coherent states, Goldstone modes, and gapping gauge degrees of freedom, can be formulated as Landau’s effective theory of the Higgs mechanism. Our lattice model encodes the microscopic details that are invisible at the purely topological level but become relevant once topological invariance is broken. Building on this perspective, I will briefly introduce a CFT factory—a novel algorithm of methodically generating 2D critical lattice models that would flow to 2D conformal fixed points in the infrared—via critical boundary conditions to 2+1D topological orders (SymTOs/SymTFTs) described by our string-net models, often called the strange correlators. We engineer these critical boundary conditions by introducing multiple competing anyon condensates in the string-net model. Our structured method generates an infinite family of critical lattice models, including both known families of CFTs and novel CFTs—including examples with exotic Haagerup symmetries. This approach points toward a broader unifying framework in which topological orders, lattice gauge theories, and conformal criticality emerge as interconnected manifestations of the same underlying structure.  

This talk is part of the Isaac Newton Institute Seminar Series series.

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