Abstract

Should we include a sum over wormhole topologies in the path integral of quantum gravity? While doing so has been very useful in the last few years, it also leads to features that are inconsistent with traditional holography, like the lack of factorization of the partition function on disconnected boundaries. In this talk, I will propose a systematic algorithm to restore factorization in a gravitational path integral with wormholes by adding nonlocal effects. There is a precise analogy between this algorithm and the BPHZ procedure from perturbative renormalization in quantum field theory, where spacetime wormholes play the role of divergences and nonlocal effects play the role of counterterms. A Hopf algebra of symmetries underlies this procedure, and the group dual to this Hopf algebra acts to reorganize the sum over topologies into various “gauge-equivalent” ways of constructing a factorizing gravitational path integral that have previously been empirically observed in the literature.