arXiv subjects

Carlos I. Pérez-Sánchez

Publications and source records attributed to Carlos I. Pérez-Sánchez.

5 recordsLinked to original sources

arXiv2026

Bootstrapping Tensor Integrals

This work proposes a bootstrapping with positivity methodology to study random $U(N)^{D}$ invariant tensors in the large $N$ limit. As has been done for $U(N)$ invariant random matrices, we combine the Dyson-Schwinger equations and positivity constraints of moments to approximate the moments of such tensor models. As examples, we bootstrap the quartic and two hexic rank three tensor models. All models studied converge quickly, and for those which have known analytic formulae, they converge to such solutions. We conjecture new explicit formulae for all moments of the rank three quartic model and support this conjecture using bootstrapped results and explicit double-series computations with 'feyntensor'.

hep-th↗

arXiv2018

The full Ward-Takahashi Identity for colored tensor models

Colored tensor models (CTM) is a random geometrical approach to quantum gravity. We scrutinize the structure of the connected correlation functions of general CTM-interactions and organize them by boundaries of Feynman graphs. For rank-$D$ interactions including, but not restricted to, all melonic $φ^4$-vertices---to wit, solely those quartic vertices that can lead to dominant spherical contributions in the large-$N$ expansion---the aforementioned boundary graphs are shown to be precisely all (possibly disconnected) vertex-bipartite regularly edge-$D$-colored graphs. The concept of CTM-compatible boundary-graph automorphism is introduced and an auxiliary graph calculus is developed. With the aid of these constructs, certain $\mathrm U(\infty)$-invariance of the path integral measure is fully exploited in order to derive a strong Ward-Takahashi Identity for CTMs with a symmetry-breaking kinetic term. For the rank-$3$ $φ^4$-theory, we get the exact integral-like equation for the 2-point function. Similarly, exact equations for higher multipoint functions can be readily obtained departing from this full Ward-Takahashi identity. Our results hold for some Group Field Theories as well. Altogether, our non-perturbative approach trades some graph theoretical methods for analytical ones. We believe that these tools can be extended to tensorial SYK-models.

math-ph↗

arXiv2018

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

Surgery in colored tensor models

Rooted in group field theory and matrix models, random tensor models are a recent background-invariant approach to quantum gravity in arbitrary dimensions. Colored tensor models (CTM) generate random triangulated orientable (pseudo)-manifolds. We analyze, in low dimensions, which known spaces are triangulated by specific CTM interactions. As a tool, we develop the graph-encoded surgery that is compatible with the structure of quantum field theory and use it to prove that a single model, the complex $φ^4$-interaction in rank-$2$, generates all orientable $2$-bordisms, thus, in particular, also all orientable, closed surfaces. We show that certain quartic rank-$3$ CTM, the $φ_3^4$-theory, has as boundary sector all closed, possibly disconnected, orientable surfaces. Hence all closed orientable surfaces are cobordant via manifolds generated by the $φ_3^4$-theory.

math-ph↗

arXiv2015

Correlation functions of just renormalizable tensorial group field theory: The melonic approximation

The $D$-colored version of tensor models has been shown to admit a large $N$-limit expansion. The leading contributions result from so-called melonic graphs which are dual to the $D$-sphere. This is a note about the Schwinger-Dyson equations of the tensorial $φ^{4}_{5}$-model (with propagator $1/{\bf p}^{2}$) and their melonic approximation. We derive the master equations for two- and four-point correlation functions and discuss their solution.

hep-th↗