String theory on curved background fields is notoriously difficult: quantum consistency of the worldsheet CFT imposes an infinite tower of constraints on the background fields, and calculations which were straightforward for flat backgrounds (e.g., writing vertex operators, computing correlators) are practically impossible. I will discuss how certain chiral, constrained worldsheet theories (known as 'ambitwistor strings') describe QFT degrees of freedom directly and avoid many of the difficulties associated with ordinary strings on curved backgrounds. As a concrete example, we will consider how ambitwistor strings could shed light on perturbation theory in plane wave backgrounds.
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