PP-Wave Light-Cone Free String Field Theory at Finite Temperature
  In this paper, a real-time formulation of light-cone pp-wave string field theory at finite temperature is presented. This is achieved by developing the thermo field dynamics (TFD) formalism in a second quantized string scenario. The equilibrirum thermodynamic quantities for a pp-wave ideal string gas are derived directly from expectation values on the second quantized string thermal vacuum. Also, we derive the real-time thermal pp-wave closed string propagator. In the flat space limit it is shown that this propagator can be written in terms of Theta functions, exactly as the zero temperature one. At the end, we show how supestrings interactions can be introduced, making this approach suitable to study the BMN dictionary at finite temperature. 
M. C. B Abdalla, A. L. Gadelha and Daniel L. Nedel