We present an explicit calculation of the one-loop quantum corrections to the mass and the two central charges of the kink solution of an N=(2,2) supersymmetric CP^1 model with twisted mass, using supersymmetry preserving dimensional regularization adapted to solitons. We find that the quantum corrections of the mass and one of the central charges are nontrivial (but saturate the BPS bound), while the other central charge receives no corrections. The nontrivial central charge correction

more »

... nds to a quantum anomaly, which in our scheme appears as parity violation in the regulating extra dimension, and its magnitude is in agreement with exact results obtained by Dorey on the basis of a massive analog of mirror symmetry from a dual U(1) gauge theory, confirming also the recent work by Shifman, Vainshtein, and Zwicky.