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Renormalization of hypercuboidal spin foams

Dec 07
4:00 pm o'clock to 5:30 pm o'clock
SR 02.729

In this talk I will present recent results on the renormalization of the
4D Euclidean EPRL spin foam model, which is restricted to be
"cuboid-shaped". To this end I will review the construction of this
restricted model, which is defined on a hypercubic 2-complex and thus
called "quantum cuboids". In order to define a renormalization group
flow I need to represent the same (physical) process, e.g. a transition,
on different discretisations, which is done by relating the states on
the boundary of the foams via embedding maps. In this restricted model,
this essentially reduces to relating coarse to fine cuboids via a
geometrical embedding map. Hence I define a renormalized amplitude,
whose properties are studied by numerically computing expectation values
of simple observables. The observables are used to project the
renormalized amplitude down to the original model resulting in a
renormalization group flow. Remarkably, this flow shows indications for
a phase transition and an UV-attractive fixed point. Furthermore it
appears that diffeomorphism symmetry might be restored on this fixed point.
This talk is based on work in collaboration with Benjamin Bahr,
arXiv:1605.07649, arXiv:1508.07961 and work in progress.