MATRIX REGULARIZATION OF N = 4 SYM ON R × S3

Abstract

We revealed a relationship between the plane wave matrix model (PWMM) and N =4 super Yang-Mills (SYM) theory on R × S3: N =4 SYM on R × S3 is equivalent to the theory around a certain vacuum of PWMM. It is suggested from this relation that N =4 SYM on R × S3 is regularized by PWMM in the planar limit. Because PWMM originally possesses the gauge symmetry and SU(2|4) symmetry, this regularization also preserves these symmetries. In order to check the validity of this matrix regularization method, we calculate the Ward identity and the beta function at the 1-loop level. We find that the Ward identity is satisfied and the beta function vanishes in the continuum limit. The former result is consistent with the gauge symmetry of PWMM. The latter suggests the possibility that the conformal symmety is restored in the continuum limit.