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キーワード:
High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc
要旨:
We tackle the issue of renormalizability for Tensorial Group Field Theories
(TGFT) including gauge invariance conditions, with the rigorous tool of
multi-scale analysis, to prepare the ground for applications to quantum gravity
models. In the process, we define the appropriate generalization of some key
QFT notions, including: connectedness, locality and contraction of (high)
subgraphs. We also define a new notion of Wick ordering, corresponding to the
subtraction of (maximal) melonic tadpoles. We then consider the simplest
examples of dynamical 4-dimensional TGFT with gauge invariance conditions for
the Abelian U(1) case. We prove that they are super-renormalizable for any
polynomial interaction.
