PIRSA:20030111

Gapped condensation in higher categories

Johnson-Freyd, T. (2020). Gapped condensation in higher categories. Perimeter Institute. https://pirsa.org/20030111

Johnson-Freyd, Theo. Gapped condensation in higher categories. Perimeter Institute, Mar. 17, 2020, https://pirsa.org/20030111 

          @misc{ pirsa_PIRSA:20030111,
            doi = {10.48660/20030111},
            url = {https://pirsa.org/20030111},
            author = {Johnson-Freyd, Theo},
            keywords = {Mathematical physics},
            language = {en},
            title = {Gapped condensation in higher categories},
            publisher = {Perimeter Institute},
            year = {2020},
            month = {mar},
            note = {PIRSA:20030111 see, \url{https://pirsa.org}}
          }

Theo Johnson-Freyd

Dalhousie University

Talk number
PIRSA:20030111
Collection
Talk Type
Subject
Abstract

Idempotent (aka Karoubi) completion is used throughout mathematics: for instance, it is a common step when building a Fukaya category. I will explain the n-category generalization of idempotent completion. We call it "condensation completion" because it answers the question of classifying the gapped phases of matter that can be reached from a given one by condensing some of the chemicals in the matter system. From the TFT side, condensation preserves full dualizability. In fact, if one starts with the n-category consisting purely of ℂ in degree n, its condensation completion is equivalent both to the n-category of n-dualizable ℂ-linear (n-1)-categories and to an n-category of lattice condensed matter systems with commuting projector Hamiltonians. This establishes an equivalence between large families of TFTs and of gapped topological phases. Based on joint work with D. Gaiotto.