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Polchinski's equation for group field theory
Author(s) -
Krajewski T.,
Toriumi R.
Publication year - 2014
Publication title -
fortschritte der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.469
H-Index - 71
eISSN - 1521-3978
pISSN - 0015-8208
DOI - 10.1002/prop.201400043
Subject(s) - renormalization group , group field theory , mathematics , group (periodic table) , field theory (psychology) , field (mathematics) , action (physics) , context (archaeology) , boundary (topology) , mathematical physics , group theory , feynman diagram , group action , mathematical analysis , physics , pure mathematics , quantum gravity , quantum mechanics , thermal quantum field theory , paleontology , quantum , biology
We derive an exact renormalization group equation in the context of (colored) group field theories. This equation describes the variation of the effective action as some of the modes of the fields are integrated out. From a combinatorial point of view, the effective action can be expressed using a boundary triangulation and the corresponding renormalization group equation identifies some of its simplexes,In group field theory, terms in the effective action are parametrized by spin networks, while the group field theory Feynman graphs correspond to spin foams. This provides a formulation of group field theories that only involves boundary graphs.