Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 51, Issue 18, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8121/aab8a8
Keywords
constructive field theory; quantum gravity; random geometry
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The loop vertex expansion (LVE) is a constructive technique using canonical combinatorial tools. It works well for quantum field theories without renormalization, which is the case of the field theory studied in this paper. Tensorial group field theories (TGFTs) are a new class of field theories proposed to quantize gravity. This paper is devoted to a very simple TGFT for rank three tensors with U(1) group and quartic interactions, hence nicknamed U(1)-T-3(4). It has no ultraviolet divergence, and we show, with the LVE, that it is Borel summable in its coupling constant.
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