Constructive Tensorial Group Field Theory I: The $U(1)-T^4_3$ Model

Vincent Lahoche (1)

1 LPT - Laboratoire de Physique Théorique d'Orsay [Orsay]

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 -. It has no ultraviolet divergence, and we show, with the LVE, that it is Borel summable in its coupling constant.

Mots clés: constructive field theory; quantum gravity; random geometry; gravitation: quantization; expansion: vertex; field theory: constructive; coupling constant; renormalization; ultraviolet; Borel transformation; U(1)

Domaines: Physique des Hautes Energies - Théorie [hep-th]

Vincent Lahoche. Constructive Tensorial Group Field Theory I: The $U(1)-T^4_3$ Model. J.Phys.A, 2018, 51 (18), pp.185403. ⟨10.1088/1751-8121/aab8a8⟩. ⟨hal-01768105⟩