Thermal Instability of Giant Graviton in Matrix Model on PP-wave Background

The thermal instability of the giant graviton is investigated within the BMN matrix model. We calculate the one-loop thermal correction of the quantum fluctuation around the trivial vacuum and giant graviton respectively. From the exact formula of the free energy we see that at low temperature the giant graviton is unstable and will dissolve into vacuum fluctuation. However, at sufficient high temperature the trivial vacuum fluctuation will condense to form the giant graviton configuration. The transition temperature of the giant graviton is determined in our calculation.