Non-Invertible Symmetries in String Theory

Recent progress in QFT has uncovered a vast generalization of the notion of symmetry, known as non-invertible symmetry. On general grounds, we expect that any exact symmetries in quantum gravity are gauge symmetries, so it is natural to ask, can non-invertible gauge symmetry (whatever that might be) exist in string theory? After reviewing the notion of non-invertible symmetry, I will discuss a clear strategy towards finding non-invertible gauge symmetries: finding non-invertible global symmetries on the string worldsheet. I will argue that such symmetries are universally broken by string loop effects, and as a result, do not lead to non-invertible gauge symmetries in quantum gravity.