Status  Confirmed 
Seminar Series  SOUTENTH 
Subjects  hepph 
Date  Friday 8 September 2017 
Time  14:30 
Institute  LPT 
Seminar Room  Amphi 1, bat 210, 2eme etage, LPT 
Speaker's Last Name  Lionni 
Speaker's First Name  Luca 
Speaker's Email Address  luca [dot] lionni [at] th [dot] upsud [dot] fr 
Speaker's Institution  LPT Orsay 
Title  Colored discrete spaces: higher dimensional combinatorial maps and quantum gravity 
Abstract  In any dimension, the Euclidean EinsteinHilbert action, which describes gravity in the absence of matter, can be discretized over random discrete spaces obtained by gluing families of polytopes together in all possible ways. In the physical limit of small Newton constant, only discrete spaces which maximize the mean curvature survive. In two dimensions, this results in a theory of random discrete spheres, which, in the continuum limit, converge towards a fractal continuous space called the Brownian sphere, which is interpreted as a quantum spacetime. In this limit, the Liouville continuous theory of twodimensional quantum gravity is recovered. Previous results in higher dimension regarded random triangulations (gluings of tetrahedra or higher dimensional generalizations) or gluings of simple building blocks of small size. For these polytopes, we recover at best the twodimensional results. This work aims at providing combinatorial tools, which would allow a systematic study of more complicated building blocks and of the continuous quantum spacetimes they generate in the continuum limit. We develop a bijection with stacked discrete surfaces and explain how it can be used to characterize the discrete spaces that survive in the physical limit of small Newton constant. 
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