CONFORMAL FIELD THEORY, QUANTUM GROUP AND BERRY PHASE

Abstract

From an analysis of the relationship between the conformal field theory in 1+1 dimension, the Chern–Simons theory in 2+1 dimension and chiral anomaly in 3+1 dimension, we study here the relationship between the central charge c, Chern–Simons coupling k and the Berry phase factor μ where the phase is given by ei2πμ which is associated with the chiral anomaly and their association with the quantum symmetry in the framework of the Landau problem of 2D electron gas in a magnetic field. A possible link between the deformation parameter q of the deformed algebra Uq( SL (2)) with these parameters is suggested. It is also shown how a Zp spin system is realized for a quantum space and the parameter p is linked up with the deformation parameter q and; in turn with the central charge c and the Berry phase factor μ. Finally some implications of this result in a statistical system are discussed.