Instantons, supersymmetric vacua, and emergent geometries

TL;DR

This paper explores instanton solutions and superpotentials in supersymmetric gauge theories and their gravity duals, revealing insights into vacuum structures, emergent geometries, and the role of Euclidean branes in the holographic context.

Contribution

It provides a detailed analysis of instantons and superpotentials in large vacuum spaces of gauge theories and their gravity descriptions, highlighting emergent dimensions and matrix eigenvalue interpretations.

Findings

Superpotential derived in weak coupling from gauge theory.

Instantons correspond to Euclidean branes wrapping cycles in gravity.

Emergence of extra spatial dimensions in gravity duals.

Abstract

We study instanton solutions and superpotentials for the large number of vacua of the plane-wave matrix model and a 2+1 dimensional Super Yang-Mills theory on $R\times S^2$ with sixteen supercharges. We get the superpotential in the weak coupling limit from the gauge theory description. We study the gravity description of these instantons. Perturbatively with respect to a background, they are Euclidean branes wrapping cycles in the dual gravity background. Moreover, the superpotential can be given by the energy of the electric charge system characterizing each vacuum. These charges are interpreted as the eigenvalues of matrices from a reduction for the 1/8 BPS sector of the gauge theories. We also discuss qualitatively the emergence of the extra spatial dimensions appeared on the gravity side.