On zero-point energy, stability and Hagedorn behavior of type-IIB strings on pp-waves

Type-IIB strings on many pp-wave backgrounds, supported either by 5-form or 3-form fluxes, have negative light-cone zero-point energy. This raises the question of their stability and poses possible problems in the definition of their thermodynamic properties. After having pointed out the correct way of calculating the zero-point energy, an issue not fully discussed in literature, we show that these type-IIB strings are classically stable and have well defined thermal properties, exhibiting a Hagedorn behavior.