  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 corresponds 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.
