Ghost triality and superstring partition functions |
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| Institution: | 1. Santa Catarina State University – UDESC/College Ceavi/Campus Alto Vale, Department of Sanitary Engineering, Av. Getúlio Vargas, 2822, Bela Vista, CEP 89140-000 Ibirama, SC, Brazil;2. University of the Region of Joinville – UNIVILLE, Ecotoxicology Laboratory, Rua Paulo Malschitzki, 10, University Campus -Industrial District, CEP 89219-710 Joinville, SC, Brazil;3. Regional University of Blumenau – FURB, Graduate Program in Chemistry (PPGQ), Chromatography Laboratory, Av. São Paulo, 3250, Itoupava Seca, 89030-000, Blumenau, SC, Brazil;4. Santa Catarina State University – UDESC/College Ceavi/Campus Alto Vale, Department of Civil Engineering, Av. Getúlio Vargas, 2822, Bela Vista, CEP 89140-000 Ibirama, SC, Brazil |
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| Abstract: | In three or more space-time dimensions a heterotic string can have just four kinds of space-time supersymmetry, corresponding to the exceptional algebras E6, E7, E8 and F4. We give a simple argument why this correspondence, first observed in the context of the covariant lattice construction, holds for any heterotic superstring, no matter how it is constructed. Using the fact that SO(8) triality is an inner automorphism of the exceptional algebras, we derive a set of identities for character-valued partition functions, valid for any superstring in any space-time dimension and at any genus. These identities have exactly the structure of the Riemann identities, and are identical to the Riemann identities in the case of ten-dimensional strings. Their relavance for proving vanishing of the cosmological constant and non-renormalization theorems is discussed. |
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