arXiv subjects

Romain Pascalie

Publications and source records attributed to Romain Pascalie.

4 recordsLinked to original sources

arXiv2020

Combinatorial aspects of the Sachdev-Ye-Kitaev model

The Sachdev-Ye-Kitaev (SYK) model is a model of $q$ interacting fermions whose large N limit is dominated by melonic graphs. In this review we first present a diagrammatic proof of that result by direct, combinatorial analysis of its Feynman graphs. Gross and Rosenhaus have then proposed a generalization of the SYK model which involves fermions with different flavors. In terms of Feynman graphs, these flavors can be seen as reminiscent of the colors used in random tensor theory. Applying modern tools from random tensors to such a colored SYK model, all leading and next-to-leading orders diagrams of the 2-point and 4-point functions in the large $N$ expansion can be identified. We then study the effect of non-Gaussian average over the random couplings in a complex, colored version of the SYK model. Using a Polchinski-like equation and random tensor Gaussian universality, we show that the effect of this non-Gaussian averaging leads to a modification of the variance of the Gaussian distribution of couplings at leading order in $N$. We then derive the form of the effective action to all orders.

hep-th↗

arXiv2019

A Solvable Tensor Field Theory

We solve the closed Schwinger-Dyson equation for the 2-point function of a tensor field theory with a quartic melonic interaction, in terms of Lambert's W-function, using a perturbative expansion and Lagrange-B\"{u}rmann resummation. Higher-point functions are then obtained recursively.

math-ph↗

arXiv2017

Correlation functions of $\mathrm{U}(N)$-tensor models and their Schwinger-Dyson equations

We analyse the correlation functions of $\mathrm{U}(N)$-tensor models (or complex tensor models), which turn out to be classified by boundary graphs, and use the Ward-Takahashi identity and the graph calculus developed in [Commun. Math. Phys. (2018) 358: 589] in order to derive the complete tower of exact, analytic Schwinger-Dyson equations for correlation functions with connected boundary graphs. We write them explicitly for ranks $D=3$ and $D=4$. Throughout, we follow a non-perturbative approach to Tensor (Group) Field Theories. We propose the extension of this program to the Gurau-Witten model, a holographic tensor model based on the Sachdev-Ye-Kitaev model (SYK model).

math-ph↗

arXiv2017

Emergent Dark Energy in Classical Channel Gravity with Matter

Motivated by the recent increased interest in energy non-conserving models in cosmology, we extend the analysis of the cosmological consequences of the Classical Channel Model of Gravity (CCG). This model is based on the classical-quantum interaction between a test particle and a metric (classical) and results in a theory with a modified Wheeler-deWitt equation that in turn leads to non conservation of energy. We show that CCG applied to a cosmological scenario with primordial matter leads to an emergent dark fluid that at late times behaves as a curvature term in the Friedmann equations, showing that the late time behaviour is always dominated by the vacuum solutions. We discuss possible observational constraints for this model and that, in its current formulation, CCG eludes any meaningful constraints from current observations.

gr-qc↗