N =1 Super Virasoro Tensor Categories

Abstract We show that the category of C₁ C 1 -cofinite modules for the universal N=1 N = 1 super Virasoro vertex operator superalgebra S (c, 0) S (c, 0) at any central charge c is locally finite and admits the vertex algebraic braided tensor category structure of Huang–Lepowsky–Zhang. For central charges c^ {ns} (t) =152-3 (t+t^-1) c ns (t) = 15 2 - 3 (t + t - 1) with t Q t ∉ Q, we show that this tensor category is semisimple, rigid, and slightly degenerate, and we determine its fusion rules. For central charge c^ {ns} (1) =32 c ns (1) = 3 2, we show that this tensor category is rigid and that its simple modules have the same fusion rules as Rep\, osp (1 2) Rep osp (1 | 2), in agreement with earlier fusion rule calculations of Milas. Finally, for the remaining central charges c^ {ns} (t) c ns (t) with t Q^ t ∈ Q ×, we show that the simple S (c^ {ns} (t), 0) S (c ns (t), 0) -module