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We consider a (supersymmetric) bosonization of general commuting matter$\beta\gamma$ CFT. Unlike the conventional ghost $\beta\gamma$ CFTbosonization, which is typically described in terms of one scalar and one setof $\xi\eta$ CFT, the matter $\beta\gamma$ CFT is naturally bosonized to twoscalar CFTs. Surprisingly, there exists an independent subsector, whichsatisfies a constraint necessary for consistent bosonization, while the usualsector has a description in terms of two compact coordinates. The subsectoritself is a complete system which is equivalent to the original $\beta\gamma$CFT. Furthermore, a non-compact coordinate naturally emerges in this"non-compact subsector". As an immediate application, we consider thebosonization of matter $\beta\gamma$ CFT in the context of full string theoryand find the connection to noncritical string theories in the light-cone gauge.

Bosonization of Matter $\beta\gamma$ CFT, Non-compact Coordinate and Noncritical String Theory