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N =1 Super Virasoro Tensor Categories

Creutzig T, McRae R, Orosz Hunziker F, Yang J (2026)

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Publication Type: Journal article

Publication year: 2026

Journal

Book Volume: 407

Article Number: 73

Journal Issue: 4

DOI: 10.1007/s00220-026-05564-x

Abstract

We show that the category of C1-cofinite modules for the universal N=1 super Virasoro vertex operator superalgebra 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 cns(t)=152-3(t+t-1) with t∉Q, we show that this tensor category is semisimple, rigid, and slightly degenerate, and we determine its fusion rules. For central charge cns(1)=32, we show that this tensor category is rigid and that its simple modules have the same fusion rules as Reposp(1|2), in agreement with earlier fusion rule calculations of Milas. Finally, for the remaining central charges cns(t) with t∈Q×, we show that the simple S(cns(t),0)-module S2,2 of lowest conformal weight h2,2ns(t)=3(t-1)28t is rigid and self-dual, except possibly when t±1 is a negative integer or when cns(t) is the central charge of a rational N=1 superconformal minimal model. As S2,2 is expected to generate the category of C1-cofinite S(cns(t),0)-modules under fusion, rigidity of S2,2 is the first key step to proving rigidity of this category for general t∈Q×.

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APA:

Creutzig, T., McRae, R., Orosz Hunziker, F., & Yang, J. (2026). N =1 Super Virasoro Tensor Categories. Communications in Mathematical Physics, 407(4). https://doi.org/10.1007/s00220-026-05564-x

MLA:

Creutzig, Thomas, et al. "N =1 Super Virasoro Tensor Categories." Communications in Mathematical Physics 407.4 (2026).

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