Supersymmetric backgrounds in (1 + 1) dimensions and inhomogeneous field theory
Jeongwon Ho (Center for Quantum Spacetime, Sogang University, Seoul, 04107, Republic of Korea); O-Kab Kwon (Department of Physics, BK21 Physics Research Division, Autonomous Institute of Natural Science, Institute of Basic Science, Sungkyunkwan University, Suwon, 16419, Republic of Korea); Sang-A Park (Department of Physics, BK21 Physics Research Division, Autonomous Institute of Natural Science, Institute of Basic Science, Sungkyunkwan University, Suwon, 16419, Republic of Korea, Department of Physics, Yonsei University, Seoul, 03722, Republic of Korea); Sang-Heon Yi (Center for Quantum Spacetime, Sogang University, Seoul, 04107, Republic of Korea)
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.
