Douglas-Reutter 4d TQFT as a generalised orbifold

          @misc{ pirsa_PIRSA:24030083,
            doi = {10.48660/24030083},
            url = {https://pirsa.org/24030083},
            author = {Mulevi{\v{c}}ius, Vincentas},
            keywords = {Condensed Matter},
            language = {en},
            title = {Douglas-Reutter 4d TQFT as a generalised orbifold},
            publisher = {Perimeter Institute},
            year = {2024},
            month = {mar},
            note = {PIRSA:24030083 see, \url{https://pirsa.org}}
          }
          

Abstract

The state-sum invariants of 4d manifolds obtained from spherical fusion 2-categories due to Douglas-Reutter offer an exciting entrypoint to the study of 4d TQFTs. In this talk we will argue that these invariants arise from a TQFT, obtained by filling the trivial 4d TQFT with a defect foam. Such construction is known as a generalised orbifold, the Turaev-Viro-Barrett-Westbury (i.e. 3d state-sum) models are also known to arise in this way from the defects in the trivial 3d TQFT (a result by Carqueville-Runkel-Schaumann). Advantages of this point of view offer e.g. realisations of state-spaces, examples of domain walls and commuting-projector realisations of (3+1)-dimensional topological phases. Based on a joint project with Nils Carqueville and Lukas Müller.