Duality, partial supersymmetry, and arithmetic number theory

We find examples of duality among quantum theories that are related toarithmetic functions by identifying distinct Hamiltonians that have identicalpartition functions at suitably related coupling constants or temperatures. Weare led to this after first developing the notion of partial supersymmetry-inwhich some, but not all, of the operators of a theory have superpartners-andusing it to construct fermionic and parafermionic thermal partition functions,and to derive some number theoretic identities. In the process, we also find abosonic analogue of the Witten index, and use this, too, to obtain some numbertheoretic results related to the Riemann zeta function.Comment: 14 pages, harvmac, no figures; revised to add references, fix typos, add paragraph in Section