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2012

Schwinger-Dyson Equations in Group Field Theories of Quantum Gravity

Krajewski, Thomas

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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.

Schwinger-Dyson Equations in Group Field Theories of Quantum Gravity · Around

Built on

V. Chari and A. Pressley, A guide to quantum groups
1994
Earlier work this paper cites.
A. Connes and D. Kreimer, Renormalization in quantum field theory and the Riemann-Hilbert problem. 1. The Hopf algebra structure of graphs and the main theorem
2000
Earlier work this paper cites.
L. Freidel, Group field theory: An Overview
2005
Earlier work this paper cites.

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C. Rovelli, Quantum gravity
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R. Gurau, Colored Group Field Theory’
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J. Ben Geloun and V. Rivasseau, A Renormalizable 4-Dimensional Tensor Field Theory
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V. Bonzom, Revisiting random tensor models at large N via the Schwinger-Dyson equations
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Cited in the paper.

Then

R. Gurau, The complete 1/N expansion of colored tensor models in arbitrary dimensions
Original
2012
Closest in time.
R. Gurau, Nucl. Phys. B 865
Original
2012
Closest in time.

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