Emergent geometry from q-deformations of N=4 super Yang-Mills

TL;DR

This paper explores how BPS states in a q-deformed super Yang-Mills theory can be described by eigenvalue distributions that have a geometric interpretation, extending to non-BPS states and matching string theory predictions.

Contribution

It introduces a geometric eigenvalue distribution framework for BPS states in q-deformed super Yang-Mills, including non-BPS excitations and BMN limit analysis.

Findings

Eigenvalue distributions encode spacetime geometry.

The framework matches orbifold string state quantum numbers.

BMN energy computed to all orders in coupling.

Abstract

We study BPS states in a marginal deformation of super Yang-Mills on R x S^3 using a quantum mechanical system of q-commuting matrices. We focus mainly on the case where the parameter q is a root of unity, so that the AdS dual of the field theory can be associated to an orbifold of AdS_5x S^5. We show that in the large N limit, BPS states are described by density distributions of eigenvalues and we assign to these distributions a geometrical spacetime interpretation. We go beyond BPS configurations by turning on perturbative non-q-commuting excitations. Considering states in an appropriate BMN limit, we use a saddle point approximation to compute the BMN energy to all perturbative orders in the 't Hooft coupling. We also examine some BMN like states that correspond to twisted sector string states in the orbifold and we show that our geometrical interpretation of the system is consistent with the quantum numbers of the corresponding states under the quantum symmetry of the orbifold.