Matrix Strings in pp-wave backgrounds from deformed Super Yang-Mills Theory

TL;DR

This paper tackles nonperturbative string dynamics in pp-wave backgrounds by deforming ten-dimensional ${\\cal N}=1$ SYM with a constant bispinor coupling $S_H$ and a bosonic completion, followed by dimensional reduction to yield matrix theory and matrix string models on pp-waves. The authors derive the general invariance conditions that relate the deformation data (such as $H$, $K[A]$, and flux/tensor fields) and obtain a broad class of deformed matrix models, including a family generalizing the CLP supernumerary SUSY constructions and a companion IKKT deformation. Through explicit reductions to 1+1 and 0+1 dimensions, they present a rich set of matrix string theories $S_{mms}=S_{ms}+S_m$ with mass/flux deformations and analyze their supersymmetry constraints, strong-coupling behavior, and potential holographic connections. A concrete subset yields four models labeled by $(\\eta,\\eta')$, breaking $SO(8)$ to $SO(3)\\times SO(4)$ and exhibiting controlled partial supersymmetry breaking, thus providing a versatile framework for studying string interactions in pp-wave spacetimes.

Abstract

We formulate matrix models for strings in ten dimensional pp-wave backgrounds and for particles in eleven dimensional ones. This is done by first characterizing the deformations of ten dimensional {\cal N}=1 SYM which are induced by a constant bispinorial coupling $\int \barΨHΨ$ plus a minimal purely bosonic completition and then by the appropriate dimensional reduction. We find a whole class of new models for the matrix strings and a generalization of the supernumerary supersymmetric models as far as the matrix theory for particles is concerned. A companion deformation of the IKKT matrix model is also discussed.