The breakdown torque is the maximum torque which can be developed by the rotor before it overheats. The breakdown torque needs to be high for loads with high inertia and which are susceptible to overloads such as conveyor belts.
The full load torque is the torque produced by a motor operating at the rated speed and load. Exceeding the full load torque causes reduction in the life of the motor.
When the motor is run on no load, the rotor speed reaches the synchronous speed. The slip becomes zero and the motor runs at zero torque