An induction motor needs current flowing in the rotor conductors in order for there to be a torque reaction with the stator current.
In order for there to be current in the rotor conductors there must be a voltage potential.
The only way to get that potential in an induction motor is to have the rotor conductors experience a constantly changing magnetic field as in
E = -dφ/dt.
If the rotor is turning at the same speed as the flux is traveling around the stator, then each rotor conductor 'sees' a constantly fixed value of flux; meaning dφ is equal to zero, and so e must be zero.
Zero e means zero current and zero current means zero torque. To maintain synchronous speed at no load, you still need some torque to overcome the losses of friction, windage and magnetic hysteresis and eddy currents.
At no load, a motor will slow just enough to develop a little bit of rotor current to maintain rotation against the losses.