2023-08-25 Seminar Report

The fourth set of intensive lectures organised by the iTHEMS Quantum Gravity Gatherings study group has now concluded. Approximately 15 participants joined this three day event in which we were given a comprehensive overview of the causal dynamical triangulations (CDT) approach to 2D quantum spacetime. Leading affairs was Dr Yuki Sato of the National Institute of Technology, Tokuyama College, who presented in a tightly organised and very pedagogical manner. Following some brief motivations for the CDT approach to quantum gravity and a summary of the numerical understanding of the theory in 4D, Sato-san began with an overview of discrete geometry in Lorentzian spaces and used this to introduce Lorentzian Regge calculus. The fundamental idea here is to realise curvature as a conical defect at certain codimension 2 regions of piecewise-flat manifolds. We concluded the first day by using this to construct the Lorentzian Einstein-Regge action in arbitrary dimension before specialising to the 2D case. We began the second day by explicitly quantising this 2D action and then proceeded to take its continuum limit, allowing for the deduction of the quantum Hamiltonian of the theory. We then briefly covered the formalism of 2D projectable Hořava–Lifshitz (PHL) gravity and demonstrated the equivalence of this theory to 2D CDT by showing that PHL gravity is described by the same Hamiltonian as in the CDT case. On the third day we learnt about a generalisation of the 2D CDT model allowing for topology change to occur, employing ideas from string field theory in the process; we studied a dual matrix model representation of the theory and derived an effective quantum Hamiltonian including the contribution of such wormhole configurations. Finally we saw how topology change in 2D generalised CDT could be realised in terms of stochastic time-dependent fluctuations of the cosmological constant in line with the so-called Coleman mechanism. In addition to the scientific activities above we had a number of short talks on the first and second days of the event by participants as well as a banquet on the first day where we were joined by several iTHEMS members. The intimate nature of the event lead to the active participation of attendees and overall a very lively and productive learning environment.

Reported by Christy Koji Kelly

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