Related papers: Resurgent transseries $\&$ Dyson-Schwinger equatio…
We analyze the vacuum expectation values of conserved charges in two dimensional integrable theories. We study the situations when the ground-state can be described by a single integral equation with a finite support: the thermodynamic…
Neural network field theory (NN-FT) formulates field theory in terms of a network architecture and a density on its parameters. We derive Schwinger--Dyson equations and Ward identities in NN-FT and utilize them to study anomalies. The…
The realization of a nonlocal quantum field theory without losing unitarity, gauge invariance and causality is investigated. It is commonly retained that such a formulation is possible at tree level, but at quantum level acausality…
Two examples of recent progress in applications of the Dyson-Schwinger equation (DSE) formalism are presented: (1) Strong coupling quantum electrodynamics in 4 dimensions (QED$_4$) is an often studied model, which is of interest both in its…
In the leading order of a modified 1/Nc expansion, we show that a class of gauge-Higgs-Yukawa systems in four dimensions give non-trivial and well-defined theories in the continuum limit. The renormalized Yukawa coupling y and the quartic…
We investigate some aspects of the self-consistency in the Dyson-Schwinger approach to both the QED and the self-interacting scalar field theories. We prove that the set of the Dyson-Schwinger equations, together with the…
We study a one-dimensional chain of corner-sharing triangles with antiferromagnetic Ising interactions along its bonds. Classically, this system is highly frustrated with an extensive entropy at T = 0 and exponentially decaying spin…
We consider gauge field theories in $D>4$ following the Wilson RG approach and show that they possess the ultraviolet fixed points where the gauge coupling is dimensionless in any space-time dimension. At the fixed point the anomalous…
Extending tensor models at the field theoretical level, tensor field theories are nonlocal quantum field theories with Feynman graphs identified with simplicial complexes. They become relevant for addressing quantum topology and geometry in…
We study possible hints towards confinement in a Z$_2$-invariant Yukawa system with massless fermions and a real scalar field in the strongly-coupled regime. Using the tools developed for studying non-perturbative physics via Jacobi…
We propose a systematic analysis of Alim-Yau-Zhou's double scaling limit and Couso-Santamar\'{i}a's large radius limit for the perturbative free energies in B-model topological string theory based on \'Ecalle's Resurgence Theory. Taking…
Anomalies in transverse Ward--Takahashi identities are studied, allowing discussion of the feasibility of anomalies arising in general non-symmetry Ward--Takahashi identities. We adopt the popular Fujikawa's method and rigorous dimensional…
In the strong Yukawa coupling limit the renormalization of trilinear couplings $A_i(t)$ and combinations of the scalar particle masses $\mathfrak{M}_i^2(t)$ are studied in the framework of the Next--to--Minimal SUSY Model. The dependence of…
Sub-horizon perturbations in scalar-tensor theories have been shown to grow generically faster than in uncoupled models due to a positive, additive Yukawa force. In such cases, the amount of clustering becomes larger than in the standard…
We show how the renormalons emerge from the renormalization group equation with a priori no reference to any Feynman diagrams. The proof is rather given by recasting the renormalization group equation as a resurgent equation studied in the…
We explore whether perturbative interacting fixed points in matter systems can persist under the impact of quantum gravity. We first focus on semi-simple gauge theories and show that the leading order gravity contribution evaluated within…
Dyson-Schwinger equations (DSEs) are a non-perturbative way to express n-point functions in quantum field theory. Working in Euclidean space and in Landau gauge, for example, one can study the quark propagator Dyson-Schwinger equation in…
Effective field theory provides a new perspective on the predictive power of Renormalization Group fixed points. Critical trajectories between different fixed points confine the regions of UV-complete, IR-complete, as well as conformal…
In this work, we introduce a modification of the Dyson series based on the perturbative unitarity as a starting point. The presented approach systematically avoids singularities and double-counting related to the presence of unstable…
This paper discusses the relationships between gauge theories defined by gauge groups with finite trivially-acting centers, and theories with restrictions on nonperturbative sectors, in two and four dimensions. In two dimensions, these…