ABSTRACT
This chapter focuses on the implications of space-time non-commutativity for the causal structure of quantum string theory. Since a causality talk is possible in this non-commutative setting, one might find a perspective from which the theory's background independence can be argued along an argumentative line different from the main one followed so far. The chapter analyzes the nature of the conditions under which space-time non-commutativity arises in quantum string theory. Non-commutative field theories are field theories over a spacetime equipped with a non-commutative geometry. The ordinary notion of space, the one in which spatial coordinates commute, is usually described by the Euclidean metric. In the case of space-space non-commutativity, the field theory is not local in space but local in time. According to Nathan Seiberg, Nicolaos Toumbas, and Leonard Susskind, space-time noncommutativity seems to be an extrinsic feature of string theory since space and time fail to commute only in some specific cases.
