Abstract

The analytic continuation from Lorentzian to Euclidean signature is a well-developed tool in quantum (field) theory. Since the Euclidean path integral may have relevant complex saddle points, complexified spacetimes have come into focus recently following work by Witten. Multiple-time signatures have also been contemplated, both in the context of higher-dimensional theories (F-theory, S-theory) as well as in four dimensions (Self-dual Yang-Mills and gravity, gauge theories based on Lie supergroups, string theory with local N=2 worldsheet supersymmetry).  Non-Lorentzian signatures and complexified spacetimes are generally accepted as technical tools, but in the context of quantum gravity one may well consider spacetime signature as dynamical. Examples are Hawking’s no-boundary proposal and type-II superstring theories. In this talk I will review the reasons why non-Lorentzian signatures and dynamical signature change may exist in string theory despite the obvious conceptual issues this poses. After presenting a selection of recent results, which were obtained in joint work with Louis Gall, Giacomo Pope and Maxime Medevielle, I’ll try to clearly formulate open problems which may be amenable to methods from the areas of integrability and deep learning.