Talks

  • Dario Benedetti: "2PI effective action for tensor models "

Motivated by the central role that a bilocal action formulation has in the SYK model and its holographic interpretation, I will introduce the two-particle-irreducible (2PI) effective action for tensor models, and show that it plays a similar role. In particular, I will discuss the 1/N expansion of the Gurau-Witten model up to fourth order, and its interpretation as the one-loop approximation for an auxiliary bilocal theory.

  • Valentin Bonzom: "The large N limit of 3D tensor models with planar interaction"

The observables and the possible interactions of tensor models can be interpreted as spacetime building blocks which are completely characterized by their boundary triangulations. In 3D, the interactions are thus characterized by 2D triangulations. In particular, the corresponding building block is a 3-ball if and only if its boundary is a planar triangulation and a tensor model using such building blocks as interactions is said to have planar interactions. After detailing what makes a large N limit non-trivial in tensor models, I will show that non-trivial large N limits exist for models with planar interactions. The graphs contributing at large N have the topology of the 3-sphere and can be completely characterized by 2-point functions. It results that the large N limit of any observable is Gaussian. This can also be seen as a rigourous derivation of the universality of the branched polymer phase of observed in dynamical triangulations.

  • Sylvain Carrozza: "A large N expansion for irreducible O(N) tensor models"

​Most of the literature on tensor models focuses on tensor degrees of freedom transforming under r independent copies of a symmetry group G, one for each index (for definiteness, I will focus on r=3 and G=O(N)). This large symmetry plays a crucial role in the analysis of the 1/N expansion, so much so that it was generally believed to be essential to its existence. After summarizing these results, I will outline the recent proof that irreducible O(N) tensors (e.g. symmetric traceless ones) also support a melonic 1/N expansion. This in particular confirms a conjecture recently put forward by Klebanov and Tarnopolsky, which had only been checked numerically up to order 8 in perturbative expansion.

  • Alicia Castro: "FRGE for a 2D-CDT matrix model"

In this talk I will present how to apply the FRGE to a Matrix Model that describes Causal Dynamical Triangulations in 2D (introduced in arXiv:0812.4261), in order to compare this results with the non-causal ones (obtained in arXiv:1309.1690v1 ).

  • Antonio D. Pereira: "Functional renormalization group for rank-3 tensorial group field theory revisited"

In this talk I will discuss the complete (momentum independent) quartic order truncation of the effective average action of a real Abelian rank-3 tensorial group field theory. The truncation is said complete due to the inclusion of non-melonic as well as multi-trace interactions. Naively, in the usual functional renormalization group perspective, the inclusion of more operators that belong to the underlying theory space corresponds to an "improvement" of the truncation of the effective average action. We show that such an enlargement of the truncation brings subtleties coming from the multi-trace operator. Some perspectives on how to circumvent these issues will be debated.

  • Astrid Eichhorn: "FRG for discrete models: the causal set case"
  • Johannes Lumma: "FRG for a real rank-3 tensor model"

We consider a model of real tensors whose indices transform under different copies of the O(N) group and present how the FRG can be applied to such a model. Using the FRG we determine the running of couplings within a fourth order truncation. In particular, we find that there exists a fixed point with one relevant direction where the disconnected("multi-trace") interaction decouples from the truncation. The key to this result is distinguishing the melonic interactions by their "preferred" index, instead of using only one coupling for all quartic melonic couplings.

  • Daniele Oriti: "What I would like to understand about tensorial (group) field theories"

I will make a short list of open issues in tensorial (group) field theories that I find particularly pressing, involving both the structural aspects of these models and their renormalization. The goal is mainly to stimulate the discussion and to indicate possible directions for future collaborations.

  • Romain Pascalie: "Schwinger-Dyson equations for SYK-inspired Tensor Models"
  • Carlos Perez: "The Ward Identity and the Schwinger-Dyson equations for complex Tensor Models "

Due to the unitary symmetries implied in complex tensor models, the correlation functions of the theory turn out to be classified by boundary graphs (these are colored graphs as well). This means that the analytic Schwinger-Dyson equations do not form a tower but a pyramid. I will derive this pyramid, aided by a Ward identity, and subsequently discuss the large-N limit.

  • Andreas Pithis: "Quantum cosmology from GFT"

GFT condensate cosmology might be seen as the currently most relevant phenomenological application of tensor models. The main underlying conjecture of this approach is that continuum spacetime is a thermodynamical phase of an underlying GFT system, that is obtained through a phase transition/condensation of building blocks of the geometry. In this talk, I discuss the main aspects as well as progress and problems of the condensate cosmology picture.

  • Johannes Thürigen: "Multicritical behaviour of Tensor models up to order 6"

Tensor models generalize the matrix-model approach to 2-dimensional quantum gravity to higher dimensions. In the 1/N expansion, the simplest models generate branched-polymer geometries. Recently, enhancements yielding an additional 2d pure gravity (planar) phase and an intermediate regime of proliferating baby universes have been found. It remains an open issue to find models escaping these universality classes of low effective dimension. In this talk I will discuss the dominant regime and critical behaviour of interactions so far not considered which are candidates for such effective geometries, in particular interactions based on the utility graph. As a main result we find that, upon proper enhancement, the two-phase structure of a branched-polymer and a 2d gravity regime is the common case in U(N)-invariant tensor models. To this end I will discuss in a systematic way the enhancement scaling, the counting of leading-order diagrams and the multi-critical behaviour of a wide range of interactions, in particular for all order-6 interactions of rank 3 and 4. These findings support the claim of universality of such mixtures of branched-polymer and planar diagrams at criticality. In particular, this hints at the necessity to consider new ingredients, or interactions of higher order and rank, in order to obtain higher dimensional continuum geometry from tensor models.