Bosonization of Matter βγ CFT, Non-compact Coordinate and Noncritical String Theory
Abstract
We consider a (supersymmetric) bosonization of general commuting matter βγ CFT. Unlike the conventional ghost βγ CFT bosonization, which is typically described in terms of one scalar and one set of η CFT, the matter βγ CFT is naturally bosonized to two scalar CFTs. Surprisingly, there exists an independent subsector, which satisfies a constraint necessary for consistent bosonization, while the usual sector has a description in terms of two compact coordinates. The subsector itself is a complete system which is equivalent to the original βγ CFT. Furthermore, a non-compact coordinate naturally emerges in this "non-compact subsector". As an immediate application, we consider the bosonization of matter βγ CFT in the context of full string theory and find the connection to noncritical string theories in the light-cone gauge.