Is anti-gravity (i.e. repulsive gravity) possible in theoretical physics? Is anti-gravity (i.e. repulsive gravity) possible in string theory?
I have read some articles about scientists making assumptions about the existence of anti-gravity, but is it possible in string theory?
 A: As it happens we do observe anti-gravity (i.e. repulsive gravity) in the form of the dark energy.  There are speculative ideas to describe this from string theory, though these are far from widely accepted.
In general relativity the curvature of space time is controlled by the stress-energy tensor.  To get anti-gravity, or more precisely gravitational repulsion, you just need an appropriate stress-energy tensor.  The problem is that normal matter cannot create a stress-energy tensor of the required form: instead you require exotic matter and we have never observed this in a lab.
However you have probably heard of dark energy, which is causing the expansion of the universe to accelerate.  This does indeed create a gravitational repulsion. The trouble is that we have no idea what dark energy is.
You specifically mentioned string theory in your question, and one of the ideas from string theory is the string landscape.  One possible scenario from this is that our universe is in a metastable state, and if so this would cause a cosmological constant that behaves like the dark energy we have observed.
A: According to the String Theory, there are multiple universes or multiverses, meaning multiple dimensions and each dimension has its own frequency of existence (at least this is what I understood). 
Proponents of this theory suggest that the gravity effect we observe in our dimensional existence originated in another form from the higher dimensional existence. In the subject of 'anti-gravity' we are talking about 3 observable phenomenon in our side of dimensional existence: electrons, gravity and magnetism. If you couple electrons with gravity you got 'Electro-gravity'. If you couple electrons with magnetism you got 'Electro-magnetism' (may I excuse myself if I missed some details since this field of discussion is not really my specialization, but it is always exciting to satisfy one's curiosity in the light of new technological developments, and I always welcome other more accurate inputs from more knowledgeable sources). 
We could induce Electro-magnetic phenomenon by passing electric current along a conductive wire. If you coil the insulated conductive wire, the more turns in the coil, the greater the effect of the Electro-magnetism, just like what goes on in a regular electric motor. 
The question is about Anti-Gravity, and there was an experiment done by Thomas Townsend Brown during 1950s that exhibited anti-gravity effects for his Gravitator Disks seem to defy the gravity of the Earth by levitation upon charging each disk with at least 50 kV of DC-current. 
Brown used two parts of the disks. The upper wider area of thin conductive copper disk was charged with positive polarity and the lower lesser area of thin conductive copper disk was charged with negative. The two disks were separated by dielectric material to prevent arcing of the charges in between upper and lower disks. The disks levitated over the ground upon charging of at least 50 kV DC current.
Brown noticed that the directional movement of the disks depended upon where was the direction of the positive charged part. The directional movement of the disk when DC charged was from the negative part going towards the positive part. If you orientated the positive part at the front and the negative part at the rear, then you will have forward movement of the whole charged disks set up (please refer to the T. T. Brown pdf article from the internet).
Brown even tested his gravitator disks inside a vacuum chamber devoid with air. The disks even worked a lot better in vacuum. When fully charged, the disk would seem to glow under dim light accompanied by a hissing sound. You can say that there was not any flow of current in between the charged disks or the set up has a high voltage electro-static charge. Arcing between the two disks must be prevented for the phenomenon to be observed (levitation depending on the orientation of the positive part and negative part). The two disks had high static potential difference. The anti gravity set up would work a lot better if the DC charge on the disks were pulsed in a high frequency. By increasing the voltage you would increase the amplitude of the pulses. Increasing the amplitude means increasing the power of the disks' levitation effects.
This Anti-gravity system was already available during 1968 but the US Air Force upon seeing T. T. Brown's experiment demonstration deemed Brown's technology as Classified - and cautioned Brown to cease and desist from conducting any similar type of technologies citing National Security Concerns. Then the project went Black. No more articles were written about the said technology ever since.
