Applications and prospects of Lorentzian path integrals in quantum gravity

Lorentzian path integrals exhibit profoundly different properties from Euclidean ones due to the oscillatory integrand which weighs different configurations through interference. Key troubles encountered in Euclidean quantum gravity are the conformal factor problem of Euclidean quantum GR and divergences due to spike configurations in Euclidean quantum Regge calculus. The first part of this talk will focus on how these troubles are resolved in Lorentzian quantum Regge calculus. I will emphasize the unambiguous choice of contour for the integral over the conformal mode in a saddle-point expansion and furthermore show that bulk-length expectation values are finite for spike and spine configurations away from the classical regime.

The second part of this talk will focus on properties of Lorentzian path integrals beyond GR. I will illustrate that higher-derivative and non-local actions can be expected to suppress spacetime configurations with curvature singularities. Finally, I will revisit the long-standing question of global symmetries in quantum gravity by providing examples for non-local actions designed to suppress global-symmetry-violating black-hole configurations in the Lorentzian path integral.