Supersymmetric Deformations of Type IIB Matrix Model as Matrix Regularization of N=4 SYM

TL;DR

This paper develops a supersymmetric deformation of the type IIB matrix model that acts as a nonperturbative regularization of four-dimensional N=4 SYM, connecting matrix eigenvalues to lattice structures and D-brane configurations.

Contribution

It introduces a supersymmetry-preserving deformation of the type IIB matrix model that regularizes N=4 SYM nonperturbatively without orbifolding.

Findings

Eigenvalues lie on a hypertorus surface after deformation

Relation established between moduli space and Brillouin zone

Continuum limit recovers N=4 SYM

Abstract

We construct a $\mathcal{Q}=1$ supersymmetry and $U(1)^5$ global symmetry preserving deformation of the type IIB matrix model. This model, without orbifold projection, serves as a nonperturbative regularization for $\mathcal{N}=4$ supersymmetric Yang-Mills theory in four Euclidean dimensions. Upon deformation, the eigenvalues of the bosonic matrices are forced to reside on the surface of a hypertorus. We explicitly show the relation between the noncommutative moduli space of the deformed matrix theory and the Brillouin zone of the emergent lattice theory. This observation makes the transmutation of the moduli space into the base space of target field theory clearer. The lattice theory is slightly nonlocal, however the nonlocality is suppressed by the lattice spacing. In the classical continuum limit, we recover the $\mathcal{N}=4$ SYM theory. We also discuss the result in terms of D-branes and interpret it as collective excitations of D(-1) branes forming D3 branes.