Examples of emergent type IIB backgrounds from matrices

We study models of emergent space associated with the Coulomb branch, non-commutative and β   deformations of the N=4N=4 super-Yang–Mills theory, extending a previous work on the undeformed conformal case. The idea is to compute the effective action for D-instantons from the microscopic four-dimensional open-string description and to compare with the non-abelian D-instanton action in the dual ten-dimensional supergravity background. To linear order in the deformation parameter, the D-instantons can probe the full space–time geometry and we can derive all the supergravity fields in this way. We find a perfect match with the known supergravity solutions, including for the Neveu–Schwarz and Ramond–Ramond forms.