The Target space dependence of the Hagedorn temperature

The effect of certain simple backgrounds on the Hagedorn temperature in theories of closed strings is examined. The background of interest are a constant Neveu-Schwarz B-field, a constant offset of the space-time metric and a compactified spatial dimension. We find that the Hagedorn temperature of string theory depends on the parameters of the background. We comment on an interesting non-extensive feature of the Hagedorn transition, including a subtlety with decoupling of closed strings in the NCOS limit of open string theory and on the large radius limit of discrete light-cone quantized closed strings.