Supersymmetry at finite temperature

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Abstract
Supersymmetry at finite temperature is investigated with the use of thermo field dynamics which is a real-time quantum field theory at finite temperature. By obtaining the supersymmetric perturbation theory from the path-integral method, the Ward-Takahashi relations are shown to be satisfied at finite temperature without the need for massless particles, despite the fact that a boson field in the supermultiplet has a nonvanishing thermal average. A zero-energy mode which replaces the Goldstone mode is identified as a particle—thermal-hole pair with opposite statistics.