High Energy Theory Seminar

It has been recently recognized that the same type of melonic large N structure governs SYK models and tensor models alike. Following Witten and Klebanov-Tarnopolsky, this has led to the introduction of new SYK-like tensor models, which reproduce key features of SYK models in the familiar context of large N field theories.
Most of the literature on tensor models focuses on tensor fields transforming under r independent copies of a symmetry group G, where r is the rank of the tensor (for definiteness, I will focus on r=3 and G=O(N)). The Feynman expansion of such models is indexed by colored stranded diagrams, whose large N scalings are governed by a combinatorial quantity known as the Gurau degree. Tensor models transforming under a single copy of O(N) can be obtained by symmetrization and/or anti-symmetrization of the indices of the tensor. However, such theories turn out to generate a family of stranded diagrams with unbounded Gurau degree, which seems to preclude the construction of an interesting 1/N expansion. Nonetheless, Klebanov and Tarnopolsky recently reported compelling evidence in favour of the conjecture that symmetric tensors can actually support a melonic 1/N expansion, provided that they are also taken to be traceless. In this talk, I will outline the recent complete proof of this conjecture, and will explain why it holds more generally for arbitrary irreducible rank-3 tensor representations. Along the way, I will emphasize the crucial role of the traceless condition. I will conclude by discussing implications and possible generalizations of this result.