Supersymmetric Backgrounds in $(1+1)$ Dimensions and Inhomogeneous Field Theory

TL;DR

This paper constructs a supersymmetric background in (1+1) dimensions with a null singularity, demonstrating well-defined scalar wave propagation and connecting it to inhomogeneous field theories, while discussing quantization methods.

Contribution

It provides a new supersymmetric (1+1)-dimensional background with a null singularity and explores its implications for field theory and quantization approaches.

Findings

Scalar wave propagation is well-defined despite the null singularity.

The background relates to inhomogeneous (1+1)-dimensional field theories.

Highlights advantages of algebraic quantization over canonical methods.

Abstract

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 {\it 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.