Domain Walls, The Extended Superconformal Algebra, and The Supercurrent

TL;DR

This paper explores how domain walls necessitate a tensorial central charge extension of the superconformal algebra, constructing associated currents and analyzing their conservation and radiative corrections.

Contribution

It introduces a tensorial central charge extension of the superconformal algebra and constructs the related superconformal currents and their properties.

Findings

Superconformal algebra requires tensorial central charge extension due to domain walls.

Supercurrent contains R symmetry, SUSY, energy-momentum, and central charge currents.

Conformal tensorial central charges receive radiative corrections, unlike SUSY ones.

Abstract

The presence of a domain wall is shown to require a tensorial central charge extension of the superconformal algebra. The currents associated with the conformal central charges are constructed as spacetime moments of the SUSY tensorial central charge current. The supercurrent is obtained and it contains the R symmetry current, the SUSY spinor currents, the energy-momentum tensor and the SUSY tensorial central charge currents as its component currents. All tensorial central charge extended superconformal currents are constructed from the supercurrent. The superconformal currents' and the conformal tensorial central charge currents' (non-)conservation equations are expressed in terms of the generalized trace of the supercurrent. It is argued that although the SUSY tensorial central charges are uncorrected, the conformal tensorial central charges receive radiative corrections.