A deformation invariant of 1+1D SQFTs


Johnson-Freyd, T. (2020). A deformation invariant of 1+1D SQFTs. Perimeter Institute. https://pirsa.org/20010023


Johnson-Freyd, Theo. A deformation invariant of 1+1D SQFTs. Perimeter Institute, Jan. 14, 2020, https://pirsa.org/20010023


          @misc{ pirsa_PIRSA:20010023,
            doi = {10.48660/20010023},
            url = {https://pirsa.org/20010023},
            author = {Johnson-Freyd, Theo},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {A deformation invariant of 1+1D SQFTs},
            publisher = {Perimeter Institute},
            year = {2020},
            month = {jan},
            note = {PIRSA:20010023 see, \url{https://pirsa.org}}

Theo Johnson-Freyd Dalhousie University


The elliptic genus is a powerful deformation invariant of 1+1D SQFTs: if it is nonzero, then it protects the SQFT from admitting a deformation to one with spontaneous supersymmetry breaking. I will describe a "secondary" invariant, defined in terms of mock modularity, that goes beyond the elliptic genus, protecting SQFTs with vanishing elliptic genus. The existence of this invariant supports the hypothesis that the space of minimally supersymmetric 1+1D SQFTs provides a geometric model for universal elliptic cohomology. Based on joint works with D. Gaiotto and E. Witten.