Non-semisimple WRT as non-compact fully extended relative TQFTs

Abstract: I will argue that the Witten–Reshetikhin–Turaev-type TQFTs obtained from non-semisimple modular categories can be obtained from the Cobordism Hypothesis. This is in apparent contradiction with known results, but I will explain how one can work around these problems using relative TQFTs, following ideas of Walker, Freed–Teleman and Jordan–Safronov. I will present my recent dualizability results showing that the Cobordism Hypothesis does give a TQFT from the desired data, and conjecture that these recover the known non-semisimple TQFTs. Based on arXiv:2304.12167.

mathematical physicsalgebraic topologycategory theoryquantum algebra

Audience: researchers in the topic

Topological Quantum Field Theory Club (IST, Lisbon)

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