Supersymmetric Matrix Quantum Mechanics with Non-Singlet Sector

Abstract
We consider a supersymmetric matrix model which is related to the non-critical superstring theory. We find new non-singlet terms in the supersymmetric matrix quantum mechanics. The new non-singlet terms give rise to nontrivial interactions. These new non-singlet terms from fermions can eliminate other non-singlet terms from generators of the $U(N)$ subalgebra and from time periodicity. The non-singlet terms from the generators violate the $T$ duality on the target space, which is a circle. Therefore, we can retain the $T$ duality with a process of the elimination

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