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

Abstract

A superfield formulation is presented of the central charge anomaly in quantum corrections to solitons in two-dimensional theories with N = 1 supersymmetry. Extensive use is made of the superfield supercurrent, that places the supercurrent J µ α , energy-momentum tensor Θ µν and topological current ζ µ 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 µ α , Θ µν , ζ µ ) is kept exact while the topological current ζ µ 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.

Effect of quantum fluctuations on topological excitations and central charge in supersymmetric theories

“…This generalizes an earlier result [18] to all orders inh. We remark that via dilatation one has naturally been led to the supertrace identity for the improved supercurrent …”

“…It implies that the supersymmetry current J µ α , topological current ζ µ and energy-momentum tensor T µλ form a supermultiplet. This structure is best visualized if one considers a superfield supercurrent [16], which in the present case is a real spinor-vector superfield [18] 10) with the expansion…”

“…There one again encounters infinite renormalization only for the bare mass m up to two loops. Indeed, a direct oneloop calculation yields the effective superpotential [18] …”

Domain walls, the extended superconformal algebra and the supercurrent

“…This can be interpreted as the invariance of the theory under a local tensorial symmetry transformation involving only the auxiliary fields as found in references [15], [12]. The conserved SUSY tensorial central charge currents correspond to a local symmetry transformation of the auxiliary fields Expanding the superfield expression for the supercurrent, equation (3.12), in terms of the component fields, the identification of its components in terms of the improved currents can be made…”

“…So doing the corresponding identification of the supercurrent components is secured. This is done for the generalized Wess-Zumino model with canonical Kähler potential, usingī = i when no ambiguity arises, (3.11) In this case the supercurrent is given by 12) and the breaking terms in the trace identities are…”