Non-commutative gravity from the AdS/CFT correspondence.

The exclusion principle of Maldacena and Strominger is seen to follow from deformed Heisenberg algebras associated with the chiral rings of S-N orbifo ld CFTs. These deformed algebras are related to quantum groups at roots of unity, and are interpreted as algebras of space-time field creation and ann ihilation operators. We also propose, as space-time origin of the stringy e xclusion principle, that the AdS(3) x S-3 space-time of the associated six- dimensional supergravity theory acquires, when quantum effects are taken in to account, a non-commutative structure given by SUq (1; 1) x SUq(2). Both remarks imply that finite N effects are captured by quantum groups SLq(2) w ith q = e(i pi)/(N+1). This implies that a proper framework for the theorie s in question is given by gravity on a non-commutative spacetime with a q-d eformation of field oscillators. An interesting consequence of this framewo rk is a holographic interpretation for a product structure in the space of all unitary representations of the non-compact quantum group SUq(1; 1) at r oots of unity.