The Conformal Properties of Liouville Field Theory on Z_N-Riemann Surfaces

The Liouville field theory on Z_N-Riemann surfaces is studied and it is shown that it decomposes into a Liouville field theory on the sphere and N-1 free boson theories. Also, the partition function of the Liouville field theory on the Z_N-Riemann surfaces is expressed as a product of the correlation function for the Liouville vertex operators on the sphere and a number of twisted fields.Comment: Version to appear in Phys. Lett. B; LaTeX file, 8 pages, no figure

Chiral bosonization for non-commutative fields

A model of chiral bosons on a non-commutative field space is constructed and new generalized bosonization (fermionization) rules for these fields are given. The conformal structure of the theory is characterized by a level of the Kac-Moody algebra equal to $(1+ \theta^2)$ where $\theta$ is the non-commutativity parameter and chiral bosons living in a non-commutative fields space are described by a rational conformal field theory with the central charge of the Virasoro algebra equal to 1. The non-commutative chiral bosons are shown to correspond to a free fermion moving with a speed equal to $c^{\prime} = c \sqrt{1+\theta^2}$ where $c$ is the speed of light. Lorentz invariance remains intact if $c$ is rescaled by $c \to c^{\prime}$. The dispersion relation for bosons and fermions, in this case, is given by $\omega = c^{\prime} | k|$.Comment: 16 pages, JHEP style, version published in JHE