Supersymmetric backgrounds in (1+1) dimensions and inhomogeneous field theory

We find a (1 + 1)-dimensional metric solution for a background hosting various supersymmetric field theories with a single non-chiral real supercharge. This supersymmetric background is globally hyperbolic even though it contains a naked null singularity. In this regard, we show that scalar wave propagation on the background is well-defined and so the curvature singularity is a mild one. Taking inspiration from our previous work, we relate the field theory on this curved background to some classes of (1 + 1)-dimensional inhomogeneous field theory in the supersymmetric setup. Utilizing our supersymmetric background, we elucidate the limitations of canonical quantization and highlight the conceptual advantages of the algebraic approach to quantization.

Automated summary

In this paper, we find a metric solution for a (1 + 1)-dimensional background that hosts various supersymmetric field theories with a single non-chiral real supercharge. Despite containing a naked null singularity, this supersymmetric background is globally hyperbolic. We show that scalar wave propagation on the background is well-defined, suggesting that the curvature singularity is mild. Building on our previous work, we establish a connection between the field theory on this curved background and certain classes of (1 + 1)-dimensional inhomogeneous field theory in the supersymmetric setup. By utilizing this supersymmetric background, we demonstrate the limitations of canonical quantization and emphasize the conceptual advantages of the algebraic approach to quantization.