Examples of Emergent Type IIB Backgrounds from Matrices

TL;DR

This paper investigates how space can emerge from matrix models related to deformations of N=4 super Yang-Mills theory, matching microscopic string calculations with supergravity backgrounds.

Contribution

It extends previous work by analyzing deformed theories and deriving supergravity fields from D-instanton effective actions, confirming the emergence of known backgrounds.

Findings

Successful derivation of supergravity fields from D-instanton actions.

Matching of microscopic string theory results with supergravity solutions.

Extension of emergent space models to deformed N=4 theories.

Abstract

We study models of emergent space associated with the Coulomb branch, non-commutative and beta deformations of the N=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.