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3-Dimensional Topological QFTs from Non-Semisimple Modular Categories

QMAP Seminar

Speaker: Azat Gainutdinov, Institut Denis Poisson
Related Webpage: https://www.researchgate.net/profile/Azat_Gainutdinov
Location: 2112 MSB
Start time: Fri, Mar 13 2020, 12:00PM

The input data for the famous Reshetikhin-Turaev-Witten construction of 3d TQFTs is a modular tensor category that is assumed to be semi-simple, e.g. those categories that are made of representations from Rational 2d Conformal Field Theories. In middle of 90's Lyubashenko has proposed a reasonable non-semisimple version of modular categories and it was later shown that they produce mapping class group representations with new features not present in the RTW construction. Many important examples of such categories come from two-dimensional Logarithmic CFTs. However, a proper TQFT construction for Lyubashenko's theory was missing. In this talk, I will present our recent construction that provides such TQFTs with input data given by any not necessarily semi-simple modular category over a field.