Related papers: Brick wall diagrams as a completely integrable sys…
We introduce a general model of dimer coverings of certain plane bipartite graphs, which we call rail yard graphs (RYG). The transfer matrices used to compute the partition function are shown to be isomorphic to certain operators arising in…
We show that momentum space Feynman diagrams involving internal massless fields can be cast as conformal integrals. This leads to a classification of all Feynman diagrams into conformal families, labelled by conformal integrals. Computing…
Bi-scalar CFT from $\gamma$ deformed $\cal N$=4 SYM describes the fishnet theory which is integrable in the planar limit. The holographic dual of the planar model is the fishchain model. The derivation of the weak-strong duality from the…
A free boson on a lattice is the simplest field theory one can think of. Its partition function can be easily computed in momentum space. However, this straightforward solution hides its integrability properties. Here, we use the methods of…
Chung-Langlands established a matrix-tree theorem for positive-real valued vertex-weighted graphs, and Wu-Feng-Sato developed a theory of Ihara zeta functions for those graphs. In this paper, generalizing and refining these previous works,…
We analyze the phase diagram of the Yukawa-Sachdev-Ye-Kitaev model, which describes complex fermions randomly interacting with real bosons via a Yukawa coupling, at finite temperatures and varying fermion density. In a recent work [Phys.…
We investigate the thermodynamic properties of a novel class of gauge-Yukawa theories that have recently been shown to be completely asymptotically safe, because their short-distance behaviour is determined by the presence of an interacting…
The recently proposed low degree-of-freedom model of Moffat and Kimura [1,2] for describing the approach to finite-time singularity of the incompressible Euler fluid equations is investigated. The model assumes an initial finite-energy…
Isomorph theory is employed in order to establish a mapping between the bridge function of Coulomb and Yukawa one-component plasmas. Within an exact invariance ansatz for the bridge functions and by capitalizing on the availability of…
We explore the idea to bootstrap Feynman integrals using integrability. In particular, we put the recently discovered Yangian symmetry of conformal Feynman integrals to work. As a prototypical example we demonstrate that the D-dimensional…
Wilson-Fisher expansion near upper critical dimension has proven to be an invaluable conceptual and computational tool in our understanding of the universal critical behavior in the $\phi ^4$ field theories that describe low-energy physics…
The idealized theory of quantum vacuum energy density is a beautiful application of the spectral theory of differential operators with boundary conditions, but its conclusions are physically unacceptable. A more plausible model of a…
We develop the variational and correlated basis functions/parquet-diagram theory of strongly interacting normal and superfluid systems. The first part of this contribution is devoted to highlight the connections between the Euler equations…
The free energy of a multi-component scalar field theory is considered as a functional W[G,J] of the free correlation function G and an external current J. It obeys non-linear functional differential equations which are turned into…
Akiyama and Watanabe conjectured that every simple planar bipartite graph on $n$ vertices contains an induced forest on at least $5n/8$ vertices. We apply the discharging method to show that every simple bipartite planar graph on $n$…
A phenomenological approach to the ferromagnetic two dimensional Potts model on square lattice is proposed. Our goal is to present a simple functional form that obeys the known properties possessed by the free energy of the q-state Potts…
The brick-wall model seeks to explain the Bekenstein-Hawking entropy as a wall-contribution to the thermal energy of ambient quantum fields raised to the Hawking temperature. Reservations have been expressed concerning the self-consistency…
This paper investigates further how the presence of a single reflecting plane wall modifies the usual Planckian forms in the thermodynamics of the massless scalar radiation in $N$-dimensional Minkowski spacetime. This is done in a rather…
We introduce the notion of Wall-Crossing Structure and discuss it in several examples including complex integrable systems, Donaldson-Thomas invariants and Mirror Symmetry. For a big class of non-compact Calabi-Yau 3-folds we construct…
We present a general representation for solving problems in many-body perturbation theory. By projecting the single-particle Green's function to an auxiliary space we show how one can convert an arbitrary Feynman graph to a universal kernel…