Related papers: Higher Genus Correlators from the Hermitian One-Ma…

We reformulate the zero-dimensional hermitean one-matrix model as a (nonlocal) collective field theory, for finite~$N$. The Jacobian arising by changing variables from matrix eigenvalues to their density distribution is treated {\it…

We review a class of matrix models whose degrees of freedom are matrices with anticommuting elements. We discuss the properties of the adjoint fermion one-, two- and gauge invariant D-dimensional matrix models at large-N and compare them…

A very elementary model of a single positive hermitian random matrix coupled to an external matrix is defined and studied. Expanding the exact effective action around its classical solution leads to the ``quantum Penner action'', from which…

Unitary 1-matrix models are shown to be exactly equivalent to hermitian 1-matrix models coupled to 2N vectors with appropriate potentials, to all orders in the 1/N expansion. This fact allows us to use all the techniques developed and…

Since the ($\beta$-deformed) hermitian one-matrix models can be represented as the integrated conformal field theory (CFT) expectation values, we construct the operators in terms of the generators of the Heisenberg algebra such that the…

We compute an the genus 1 correction to free energy of Hermitian two-matrix model in terms of theta-functions associated to spectral curve arising in large N limit. We discuss the relationship of this expression to isomonodromic…

We develop a method for computing correlation functions of twist operators in the bosonic 2-d CFT arising from orbifolds M^N/S_N, where M is an arbitrary manifold. The path integral with twist operators is replaced by a path integral on a…

In this article, a model of random hermitian matrices is considered, in which the measure $\exp(-S)$ contains a general U(N)-invariant potential and an external source term: $S=N\tr(V(M)+MA)$. The generalization of known determinant…

Within the framework of the standard quantum electrodynamics, we compute contribution of vacuum polarization at one-loop order to the power spectrum of the magnetic field on inflationary (de Sitter) background. It is found that the one-loop…

Let ${\mathbb M}_{g, 1}$, $g \geq 1$, be the moduli space of triples $(C, P_0, v)$ of genus $g$, where $C$ is a compact Riemann surface of genus $g$, $P_0 \in C$, and $v \in T_{P_0}C\setminus\{0\}$. Using Chen's iterated integrals we…

We give a review of the one-loop divergences in higher derivative gravity theories. We first make the bilinear expansion in the quantum fluctuation on arbitrary backgrounds, introduce a higher-derivative gauge fixing and show that…

We introduce a parametrization of the coupling constant space of the generalized Kontsevich models in terms of a set of moments equivalent to those introduced recently in the context of topological gravity. For the simplest generalization…

In this final part of a series of three papers, we will assemble supersymmetric expressions for one-loop correlators in pure-spinor superspace that are BRST invariant, local, and single valued. A key driving force in this construction is…

The vacuum structure of the inert doublet model is analysed at the one-loop level using the effective potential formalism, to verify the validity of tree-level predictions for the properties of the global minimum. An inert minimum (with…

In this talk we go over several new developments regarding the techniques for a large class of non-hermitian matrix models with unitary randomness (complex random numbers). In particular, we discuss: (a) - A diagrammatic approach based on a…

Perturbation of the GUE are known in physics to be related to enumeration of graphs on surfaces. We investigate this idea and show that for a small convex perturbation, we can perform a genus expansion: the moments of the empirical measure…

We consider the six-vertex model on an $N \times N$ square lattice with the domain wall boundary conditions. Boundary one-point correlation functions of the model are expressed as determinants of $N\times N$ matrices, generalizing the known…

We propose a randomized algorithm to compute the log-partition function of weakly interacting fermions with polynomial runtime in both the system size and precision. Although weakly interacting fermionic systems are considered tractable for…

In this thesis, we analyze unitary conformal field theories in three dimensional spaces by applying analytic conformal bootstrap techniques to correlation functions of non-scalar operators, in particular Majorana fermions. Via the analysis…

We study fermionic one-matrix, two-matrix and $D$-dimensional gauge invariant matrix models. In all cases we derive loop equations which unambiguously determine the large-$N$ solution. For the one-matrix case the solution is obtained for an…