Massive deformations of supersymmetric Yang-Mills matrix models

TL;DR

This work classifies all supersymmetry-preserving mass deformations of SU(N) SYM matrix models in $D=3,4,6,10$, proving the polarized IKKT model is the unique deformation in $D=10$ and identifying two sign-problem-free massive models in $D=4$. It develops a deformation framework where $S=S_0+ frac{1}{g_{YM}^2}(\mu S_1+\mu^2 S_2+\dots)$ with SUSY-closure constraints, yielding complete families in $D=6$ (Type I/II), $D=4$ (Type I/II), and a two-parameter $D=3$ model, alongside the D=10 uniqueness result. The paper analyzes saddle structures, Myers terms, and residual symmetries (e.g., $SO(3)\times SO(7)$ in $D=10$, $D(2,1,\alpha)$ in $D=6$ Type I, and $OSp^*$ algebras in $D=4$), and discusses how localization or Monte Carlo could access protected observables and holographic duals. These massive SYM matrix models provide tractable toy systems for nonperturbative studies and potential connections to gravitational backgrounds via their saddle landscapes and sphere-based reductions.

Abstract

We systematically classify all supersymmetry-preserving mass deformations of SYM matrix models in all dimensions (D = 3, 4, 6, 10). In D = 10, the polarized IKKT model emerges as the only possible deformation. In D = 4, we identify two massive models without a sign problem, making them attractive candidates for non-perturbative numerical studies.