Related papers: Second and Third Order Observables of the Two-Matr…
In this paper, we introduce a family of observables for the dimer model on a bi-periodic bipartite planar graph, called pattern density fields. We study the scaling limit of these objects for liquid and gaseous Gibbs measures of the dimer…
Two-loop self-energy corrections to the bound-electron $g$ factor are investigated theoretically to all orders in the nuclear binding strength parameter $Z\alpha$. The separation of divergences is performed by dimensional regularization,…
I present results for the two-loop self-energy functions for scalars in a general renormalizable field theory, using mass-independent renormalization schemes based on dimensional regularization and dimensional reduction. The results are…
We present a second-order calculation of relativistic large-scale-structure observables in cosmological perturbation theory, specifically the "cosmic rulers and clock", which are the building-blocks of any other large-scale-structure…
We show that the correlation functions and the free energy of the formal Hermitean 1-matrix model can be described by the recently proposed Lagrangean formalism to all orders. In addition, the loop equation of this formalism is stated and…
We compute the free energy of the planar monomer-dimer model. Unlike the classical planar dimer model, an exact solution is not known in this case. Even the computation of the low-density power series expansion requires heavy and nontrivial…
Higher-order contributions to the precision observables \Delta r, \sin^2\theta_eff and \Gamma_l are discussed. The Higgs-mass dependence of the observables is investigated at the two-loop level, and exact results are derived for the…
In this training course report, I briefly present the one- and two-matrix models as tools for the study of conformal field theories with boundaries. In a first part, after a short historical presentation of random matrices, I present the…
Using the loop equations we find an explicit expression for genus 1 correction in hermitian two-matrix model in terms of holomorphic objects associated to spectral curve arising in large N limit. Our result generalises known expression for…
We present the two-loop corrected operator matrix elements calculated in N-dimensional regularization up to the finite terms which survive in the limit $\epsilon = N - 4 \to 0 $. The anomalous dimensions of the local operators have been…
In a previous work we introduced an elementary method to analyze the periodicity of a generating function defined by a single equation y=G(x,y). This was based on deriving a single set-equation Y = Gammma(Y) defining the spectrum of the…
We study higher order approximations in the renormalization group approach to matrix models. We use constraint equations on the free energy resulting from a freedom of field redefinitionsand obtain the effective beta function for a single…
We prove a refinement of Pixton's formula for the double ramification cycle with target variety which takes into account the correlator of a rubber map previously introduced by the authors. To do so, we need to: reinterpret the correlator…
Electron correlation in finite and extended systems is often described in an effective single-particle framework within the $GW$ approximation. Here, we use the statically screened second-order exchange contribution to the self-energy…
We review the number counts to second order concentrating on the terms which dominate on sub horizon scales. We re-derive the result for these terms and compare it with the different versions found in the literature. We generalize our…
An alternative formula for the partition function of the Goulden-Harer-Jackson matrix model is derived, in which the Penner and the orthogonal Penner partition functions are special cases of this formula. Then the free energy that computes…
We calculate the complete tadpoles and self-energies at the two-loop order for scalars in general renormalisable theories, a crucial component for calculating two-loop electroweak corrections to Higgs-boson masses or for any scalar beyond…
In recent years, surprise discoveries of pulsed emission from the Crab and Vela pulsars above 100 GeV have drawn renewed attention to this largely unexplored region of the energy range. In this paper, we discuss example light curves due to…
For matrix models with measure on the Lie algebra of SO/Sp, the sub-leading free energy is given by F_{1}(S)=\pm{1/4}\frac{\del F_{0}(S)}{\del S}. Motivated by the fact that this relationship does not hold for Chern-Simons theory on S^{3},…
We consider the spherical limit of multi-matrix models on regular target graphs, for instance single or multiple Potts models, or lattices of arbitrary dimension. We show, to all orders in the low temperature expansion, that when the degree…