CLASSICAL VERSUS QUANTUM SYMMETRIES FOR TODA THEORIES WITH A NONTRIVIAL BOUNDARY PERTURBATION

In this paper we present a detailed study of the quantum conservation laws for Toda field theories defined on the half plane in the presence of a boundary perturbation. We show that total derivative terms added to the currents, while irrelevant at the classical level, become impo rtant at the quantum level and in general modify significantly the qua ntum boundary conservation. We consider the first nontrivial higher-sp in currents for the simply laced a(n)((1)) Toda theories: we find that the spin-three current leads to a quantum conserved charge only if th e boundary potential is appropriately redefined through a finite renor malization. Contrary to the expectation we demonstrate instead that at spin four the classical symmetry does not survive quantization and we suspect that this feature will persist at higher-spin levels. Finally , we examine the first nontrivial conservations at spin four for the d (3)((2)) and c(2)((1)) nonsimply laced Toda theories, In these cases t he addition of total derivative terms to the bulk currents is necessar y but sufficient to ensure the existence of corresponding quantum exac t conserved charges.