Supersymmetric Matrix Model on Z-Orbifold

We find that the IIA Matrix models defined on the non-compact C/Z6, C /Z2 and C/Z4 orbifolds preserve supersymmetry where the fermions are on-massshell Majorana-Weyl fermions. In these examples supersymmetry is preserved both in the orbifolded space and in the non-orbifolded space at the same time. The Matrix model on C/Z6 orbifold has the same N = 2 supersymmetry as the case of C/Z3 orbifold, whose particular case was previously pointed out. On the other hand the Matrix models on C/Z2 and C /Z4 orbifold have a half of the N = 2 supersymmetry. We further find that the Matrix model on C/Z2 orbifold with parity-like identification preserves N = 2 supersymmetry both in the orbifolded space and non-orbifolded space, and furthermore has N = 4 supersymmetry parameters in the total space. [email protected] Introduction The dynamics of an extended objects, D-branes [1], where duality plays an impotant role, can be described in terms of the dimensionally reduced Supersymmetric Yang-Mills (SYM) Theory [2]. In particular, the dynamics of the simplest pointlike D-particles may play the fundamental role in 11d super-membrane theory[3], [4]. The dynamics of D-particles is supposed to be described by the SYM theory dimensionally reduced to one temporal dimension, that is the quantum mechanics of the SUSY Matrix model. The bosonic fields are described by the coodinates consisting of N D-particles. The bosonic and fermionic fields are represented by N ×N hermitian matrices. The 11d M-theory compactified on a simple orbifold space, S/Z2, was shown to be connected with the 10d E8 × E8 heterotic string theory [5]. While the 6d compactification on the Calabi-Yau manifold from 10d heterotic string theory was given by [6], and the compactification on the orbifold was given in [7],[8],[9]. The type IIA Matrix model on the orbifold spaces are explicitly compactified by [10], [11], [12], [13], [14], and others. The Matrix models on the non-compactified orbifold spaces are demonstrated in [15], [16]. We have supersymmetric Matrix model on C/Z3 orbifold[16]. In this paper we study supersymmetric Matrix models on C/Z6, C /Z2 and C /Z4 orbifold. We expect that supersymmetric Matrix models on one non-compact C/Zn orbifold are limited in number. We show that Majorana condition restricts the possible supersymmetric Matrix model on non-compact orbifold. IIA Matrix model We treat nN D-particles. The action of the IIA Matrix model is written as S = 1 2g2 ∫