Superfield formulation of central charge anomalies in two-dimensional supersymmetric theories with solitons

A superfield formulation is presented of the central charge anomaly in quantum corrections to solitons in two-dimensional theories with $N=1\mathrm{}$ supersymmetry. Extensive use is made of the superfield supercurrent that places the supercurrent $J_{\alpha }^{\mu },$ energy-momentum tensor ${\Theta }^{\mu \nu },$ and topological current ${\zeta }^{\mu }$ in a supermultiplet to study the structure of supersymmetry and related superconformal symmetry in the presence of solitons. It is shown that the supermultiplet structure of ${(J}_{\alpha }^{\mu },{\Theta }^{\mu \nu },{\zeta }^{\mu })$ is kept exact while the topological current ${\zeta }^{\mu }$ acquires a quantum modification through the superconformal anomaly. In addition, the one-loop superfield effective action is explicitly constructed to verify the BPS saturation of the soliton spectrum as well as the effect of the anomaly.