Emergent geometry fromq-deformations of Script N = 4 super Yang-Mills

We study BPS states in a marginal deformation of super Yang-Mills on R x S^3using a quantum mechanical system of q-commuting matrices. We focus mainly onthe case where the parameter q is a root of unity, so that the AdS dual of thefield theory can be associated to an orbifold of AdS_5x S^5. We show that inthe large N limit, BPS states are described by density distributions ofeigenvalues and we assign to these distributions a geometrical spacetimeinterpretation. We go beyond BPS configurations by turning on perturbativenon-q-commuting excitations. Considering states in an appropriate BMN limit, weuse a saddle point approximation to compute the BMN energy to all perturbativeorders in the 't Hooft coupling. We also examine some BMN like states thatcorrespond to twisted sector string states in the orbifold and we show that ourgeometrical interpretation of the system is consistent with the quantum numbersof the corresponding states under the quantum symmetry of the orbifold.Comment: 22 pages, 1 figure. v2: added references. v3:final published versio