Path integrals and state sums for general defect TQFTs

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• Kevin Walker (Microsoft (USA))
• Thursday 18 September 2025, 10:00-11:30
• Seminar Room 2, Newton Institute.

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

For homogeneous, defect-free TQF Ts, (1) n+\epsilon-dimensional versions of the theories are relatively easy to construct; (2) an n+\epsilon-dimensional theory can be extended to n+1-dimensional (i.e. the top-dimensional path integral can be defined) if certain more restrictive conditions related to handle cancellation are satisfied; and (3) applying this path integral construction to a handle decomposition of an n+1-manifold yields a state sum description of the path integral.  In this talk, I’ll show that the same pattern holds for defect TQF Ts.  The adaptation of homogeneous results to the defect setting is mostly straightforward, with the only slight difficulty being the purely topological problem of generalizing handle theory to manifolds with defects.  If time allows, I’ll describe two applications: a Verlinde-like dimension formula for the dimension of the ground state of fracton systems, and a generalization, to arbitrary dimension, of Ostrik’s theorem relating algebra objects to modules (gapped boundaries).

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

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