The gravitational Wilson loop and the non-Abelian Stokes' theorem

          @misc{ scivideos_PIRSA:19110086,
            doi = {10.48660/19110086},
            url = {https://pirsa.org/19110086},
            author = {Toriumi, Reiko},
            keywords = {Cosmology, Quantum Fields and Strings, Quantum Gravity},
            language = {en},
            title = {The gravitational Wilson loop and the non-Abelian Stokes{\textquoteright} theorem},
            publisher = {Perimeter Institute for Theoretical Physics},
            year = {2019},
            month = {nov},
            note = {PIRSA:19110086 see, \url{https://scivideos.org/pirsa/19110086}}
          }
          

Abstract

Finding suitable diffeomorphism-invariant observables to probe gravity at the Planck scale is essential in quantum gravity. The Wilson loop of the 4-dimensional Christoffel connection is a potentially interesting ingredient for the construction of such an observable. We have investigated to what extent and what form of curvature information of the underlying spacetime may be extracted from Wilson loops through a Stokes’ theorem-like relation. We present an expression for the conservation of geometric flux as the quantity related to the gravitational Wilson loop. This expression is surface-independent and it holds for a certain class of manifolds with global symmetries.