Schwinger-Dyson Equations in Group Field Theories of Quantum Gravity

Abstract

In this talk, we elaborate on the operation of graph contraction introduced by Gurau in his study of the Schwinger-Dyson equations. After a brief review of colored tensor models, we identify the Lie algebra appearing in the Schwinger-Dyson equations as a Lie algebra associated to a Hopf algebra of the Connes-Kreimer type. Then, we show how this operation also leads to an analogue of the Wilsonian flow for the effective action. Finally, we sketch how this formalism may be adapted to group field theories.

talk given at "The XXIX International Colloquium on Group-Theoretical Methods in Physics", Chern Institute of Mathematics August 2012, submitted to the conference proceedings