



02117nas a2200157   4500008004100000245008300041210006900124260001400193490000800207520162900215100002301844700001601867700001801883700002101901856003701922       2022                        eng d00aClassification of (2+1)D invertible fermionic topological phases with symmetry0 aClassification of 21D invertible fermionic topological phases wi  c5/30/20220 v1053 a<p>We provide a classification of invertible topological phases of interacting fermions with symmetry in two spatial dimensions for general fermionic symmetry groups Gf and general values of the chiral central charge c&minus;. Here Gf is a central extension of a bosonic symmetry group Gb by fermion parity, (&minus;1)F, specified by a second cohomology class [ω2]&isin;H2(Gb,Z2). Our approach proceeds by gauging fermion parity and classifying the resulting Gb symmetry-enriched topological orders while keeping track of certain additional data and constraints. We perform this analysis through two perspectives, using G-crossed braided tensor categories and Spin(2c&minus;)1 Chern-Simons theory coupled to a background G gauge field. These results give a way to characterize and classify invertible fermionic topological phases in terms of a concrete set of data and consistency equations, which is more physically transparent and computationally simpler than the more abstract methods using cobordism theory and spectral sequences. Our results also generalize and provide a different approach to the recent classification of fermionic symmetry-protected topological phases by Wang and Gu, which have chiral central charge c&minus;=0. We show how the 10-fold way classification of topological insulators and superconductors fits into our scheme, along with general non-perturbative constraints due to certain choices of c&minus; and Gf. Mathematically, our results also suggest an explicit general parameterization of deformation classes of (2+1)D invertible topological quantum field theories with Gf symmetry.&nbsp;</p>1 aBarkeshli, Maissam1 aChen, Yu-An1 aHsin, Po-Shen1 aManjunath, Naren  uhttps://arxiv.org/abs/2109.11039