Partial symmetries of braided categories and fusion of gapped boundaries in topological orders

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• Dmitri Nikshych (University of New Hampshire)
• Monday 20 October 2025, 10:00-11:30
• Seminar Room 2, Newton Institute.

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

Let B be a modular (i.e., non-degenerate braided) tensor category describing the bulk topological order of a (2+1)-dimensional gapped phase.It is known that the group of invertible domain walls in this bulk is isomorphic to the group of braided autoequivalences of B,  representing its global topological symmetries.I will explain how this result extends beyond the invertible case: partial symmetries of B, modeled by braided lax endofunctors, correspond to gapped boundary conditions that are not necessarily invertible. In this framework, the fusion of boundaries arises from the composition of such functors, providing a natural categorical mechanism for describing and classifying non-invertible boundary phases of the topological order.

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

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