Famously, Klein and Einstein were embroiled in an epistolary dispute over whether General Relativity has any physically meaningful conserved quantities. This chapter explores the consequences of Noether’s second theorem for this debate and connects it to Einstein’s search for a ‘substantive’ version of general covariance as well as his quest to extend the Principle of Relativity. The chapter’s argument is that Noether’s second theorem provides a clear way to distinguish between theories in which gauge or diffeomorphism symmetry is doing real work in defining charges, as opposed to cases in which this symmetry stems from Kretchmannization. Finally, a comment is made on the relationship between this Noetherian form of substantive general covariance and the notion of ‘background independence’.

After a general discussion of string amplitudes we compute the 4-scalar amplitude and discuss properties of the 4-graviton amplitude, such as resonances and Regge trajectories. Then we introduce background fields and briefly discuss world-sheet beta functions and marginal deformations. We explain how effective actions can be obtained from either scattering amplitudes or beta functions. The string frame and Einstein frame are introduced and the universal part of the string effective action for graviton, Kalb–Ramond field, and dilaton is given. We also discuss background independence.