Related papers: All genus correlation functions for the hermitian …

In these notes we explain how the CFT description of random matrix models can be used to perform actual calculations. Our basic example is the hermitian matrix model, reformulated as a conformal invariant theory of free fermions. We give an…

We show how to calculate correlation functions of two matrix models. Our method consists in making full use of the integrable hierarchies and their reductions, which were shown in previous papers to naturally appear in multi--matrix models.…

The microscopic correlation functions of non-chiral random matrix models with complex eigenvalues are analyzed for a wide class of non-Gaussian measures. In the large-N limit of weak non-Hermiticity, where N is the size of the complex…

The diagrammatic coaction maps any given Feynman graph into pairs of graphs and cut graphs such that, conjecturally, when these graphs are replaced by the corresponding Feynman integrals one obtains a coaction on the respective functions.…

We give a complete description of the genus expansion of the one-cut solution to the generalized Penner model. The solution is presented in a form which allows us in a very straightforward manner to localize critical points and to…

We summarize the recent results about complete solvability of Hermitian and rectangular complex matrix models. Partition functions have very simple character expansions with coefficients made from dimensions of representation of the linear…

In hypercube approach to correlation functions in Chern-Simons theory (knot polynomials) the central role is played by the numbers of cycles, in which the link diagram is decomposed under different resolutions. Certain functions of these…

We derive the loop equations for the d-dimensional n-Hermitian matrix model. These are a consequence of the Schwinger-Dyson equations of the model. Moreover we show that in leading order of large $N$ the loop equations form a closed set. In…

We show that correlators of the hermitian one-Matrix model with a general potential can be mapped to the counting of certain triples of permutations and hence to counting of holomorphic maps from world-sheet to sphere target with three…

We consider correlation functions of topologically twisted, $\mathcal{N}=2$ supersymmetric Yang-Mills theory with gauge group ${\rm SU}(2)$ and $N_f\leq 3$ massive hypermultiplets in the fundamental representation. For a smooth, compact,…

We introduce a hierarchy of closed equations for charge density correlation functions in the Hubbard model and $2 + 1$ dimensional QED. Each step in the hierarchy can be considered a large $N$ truncation of an exact, but infinite set of…

We study the quasiclassical expansion associated with a complex curve. In a more specific context this is the 1/N expansion in U(N)-invariant matrix integrals. We compare two approaches, the CFT approach and the topological recursion, and…

We investigate supereigenvalue models in the Ramond sector and their recursive structure. We prove that the free energy truncates at quadratic order in Grassmann coupling constants, and consider super loop equations of the models with the…

Integrable theory is formulated for correlation functions of characteristic polynomials associated with invariant non-Gaussian ensembles of Hermitean random matrices. By embedding the correlation functions of interest into a more general…

In this talk, we are concerned with the formulation and understanding of the combinatorics of time-ordered n-point functions in terms of the Hopf algebra of field operators. Mathematically, this problem can be formulated as one in…

We solve the loop equations of the $\beta$-ensemble model analogously to the solution found for the Hermitian matrices $\beta=1$. For \beta=1$, the solution was expressed using the algebraic spectral curve of equation $y^2=U(x)$. For…

This paper provides an extension of the constructive loop vertex expansion to stable matrix models with interactions of arbitrarily high order. We introduce a new representation for such models, then perform a forest expansion on this…

We derive the connected correlation functions for eigenvalues of large Hermitian random matrices with independently distributed elements using both a diagrammatic and a renormalization group (RG) inspired approach. With the diagrammatic…

Using diagrammatic techniques, we provide explicit functional relations between the cumulant generating functions for the biunitarily invariant ensembles in the limit of large size of matrices. The formalism allows to map two distinct areas…

A formalism based on the fermionic functional-renormalization-group approach to interacting electron models defined on a lattice is presented. One-loop flow equations for the coupling constants and susceptibilities in the particle-particle…