Complex critical points and curved geometries in Lorentzian EPRL spinfoam amplitude

 Tuesday, October 5th

Dongxue Qu, Florida Atlantic University

Complex critical points and curved geometries in Lorentzian EPRL spinfoam amplitude
PDF of the talk (3M)
Audio+Slides of the talk (390M)
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By Jorge Pullin, LSU

The states of quantum gravity in the loop representation are given by spin networks. These are multivalent graphs with a number associated with each line. Spin foams represent the transition from an initial spin network state to a final one, as show in the figure (credit: Alejandro Perez). The expanded picture on the right is what is known as a "vertex", where new lines in the spin network are created as it transitions forward in time (time is the vertical axis). These diagrammatics correspond to precise mathematical 

equations that embody the dynamics of general relativity at a quantum level. One of the proposals for the vertex is the "EPRL" one (after Engle, Pereira, Rovelli and Livine). There has been controversy over the years about if the vertex correctly encoded the dynamics of general relativity. That requires studying how it behaves in the classical limit, as one expects departures from classical general relativity in situations where quantum effects are important. Previous calculations, done within certain approximations, seemed to suggest that curved geometries were not properly captured by this construction. The talk was about recent numerical results that imply that indeed it does capture the dynamics of classical general relativity in appropriate situations. Connections were made with a discretization of classical general relativity proposed by Tullio Regge known as Regge calculus. This is a very encouraging result indicating that the dynamics of classical general relativity is properly being captured by the "EPRL vertex".