Instantons of M(atrix) Theory in PP-Wave Background

TL;DR

This paper studies instanton solutions in M(atrix) theory within a PP-wave background, revealing their properties, zero modes, and effects on higher-order interactions, including extensions to theories with fivebranes.

Contribution

It provides the first explicit construction of instanton solutions and zero modes in M(atrix) theory on a PP-wave background, and explores their effects on effective interactions and extensions to massive theories.

Findings

Instanton solutions interpolate between supersymmetric vacua.

Supersymmetry prevents direct vacuum mixing but allows instanton effects in higher-order interactions.

Zero modes, including Goldstone modes, are explicitly constructed and analyzed.

Abstract

M(atrix) theory in PP-wave background possesses a discrete set of classical vacua, all of which preserves 16 supersymmetry and interpretable as collection of giant gravitons. We find Euclidean instanton solutions that interpolate between them, and analyze their properties. Supersymmetry prevents direct mixing between different vacua but still allows effect of instanton to show up in higher order effective interactions, such as analog of v^4 interaction of flat space effective theory. An explicit construction of zero modes is performed, and Goldstone zero modes, bosonic and fermionic, are identified. We further generalize this to massive M(atrix) theory that includes fundamental hypermultiplets, corresponding to insertion of longitudinal fivebranes in the background. After a brief comparison to their counterpart in AdS\times S, we close with a summary.