Anomaly constraint on chiral central charge of (2+1)d topological order

In this short paper, we argue that the chiral central charge c− of a (2+1)d topological ordered state is sometimes strongly constrained by 't Hooft anomaly antiunitary global symmetry. For example, if fermionic quantum field theory (TQFT) has time-reversal with T2=(−1)F labeled as ν∈Z16, TQFT must have c−=1/4 mod 1/2 for odd ν, while c−=0 even ν. This generalizes fact bosonic T in particular class carry c−=4 8 to cases. We also study such constraint U(1)×CT symmetry, which regarded gapped surface superconductor AIII.Received 5 January 2021Revised 16 March 2021Accepted 12 April 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.023107Published American Physical Society under terms Creative Commons Attribution 4.0 International license. Further distribution work maintain attribution author(s) and published article's title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)Research AreasSymmetry protected statesTopological theoriesTopological superconductorsCondensed Matter, Materials & Applied Physics