Related papers: Conformal Field Theory Techniques in Random Matrix…

We propose a random matrix model as a representation for $D=1$ open strings. We show that the model is equivalent to $N$ fermions with spin in a central potential that also includes a long-range ferromagnetic interaction between the…

This paper is primarily intended as an introduction for the mathematically inclined to some of the rich algebraic combinatorics arising in for instance CFT. It is essentially self-contained, apart from some of the background motivation and…

Two-dimensional conformal field theory (CFT) has several sources: the search for simple examples of quantum field theory, the description of surface critical phenomena, the study of (super)string vacua. In the present overview of the…

We introduce a framework for two-dimensional conformal field theory (CFT) in the language of analytic number theory. Attached to the torus partition function of every two-dimensional CFT is a self-dual, degree-4 $L$-function of root number…

The conformal field theory on a Z_N-surface is studied by mapping it on the branched sphere. Using a coulomb gas formalism we construct the minimal models of the theory.

We generalize the results of [Comm. Math. Phys. 299 (2010), 825-866, arXiv:0911.3731] (hidden Grassmann structure IV) to the case of excited states of the transfer matrix of the six-vertex model acting in the so-called Matsubara direction.…

Conformal field theory, describing systems with scaling symmetry, plays a crucial role throughout physics. We describe a quantum algorithm to simulate the dynamics of conformal field theories, including the action of local conformal…

Starting from Gaussian random matrix models we derive a new supermatrix field theory model. In contrast to the conventional non-linear sigma models, the new model is applicable for any range of correlations of the elements of the random…

The standard perturbation theory in QFT and lattice models leads to asymptotic expansions. However, an appropriate regularization of the path or lattice integrals allows one to construct convergent series with an infinite radius of the…

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…

Sparse non-Hermitian random matrices arise in the study of disordered physical systems with asymmetric local interactions, and have applications ranging from neural networks to ecosystem dynamics. The spectral characteristics of these…

Neural Network Field Theories (NN-FTs) represent a novel construction of arbitrary field theories, including those of conformal fields, through the specification of the network architecture and prior distribution for the network parameters.…

We initiate an approach to constraining conformal field theory (CFT) data at finite temperature using methods inspired by the conformal bootstrap for vacuum correlation functions. We focus on thermal one- and two-point functions of local…

We propose a new formalism for quantum field theory which is neither based on functional integrals, nor on Feynman graphs, but on marked trees. This formalism is constructive, i.e. it computes correlation functions through convergent rather…

A (1+1)D unitary bosonic rational conformal field theory (RCFT) may be organized according to its genus, a tuple $(c,\mathscr{C})$ consisting of its central charge $c$ and a unitary modular tensor category $\mathscr{C}$ which describes the…

We develop a supersymmetric field theoretical description of the Gaussian ensemble of the almost diagonal Hermitian Random Matrices. The matrices have independent random entries H_{ij} with parametrically small off-diagonal elements…

We construct fermionic conformal field theories (CFTs) whose spectra are characterized by quantum stabilizer codes. We exploit our construction to search for fermionic CFTs with supersymmetry by focusing on quantum stabilizer codes of the…

We review the algebraic and analytic aspects of the conformal field theory (CFT) and its relation to the stochastic Loewner evolution (SLE) in an example of the Ising model. We obtain the scaling limit of the correlation functions of Ising…

By using Araki's relative entropy, Lieb's convexity and the theory of singular integrals, we compute the mutual information associated with free fermions, and we deduce many results about entropies for chiral CFT's which are embedded into…

The BC-type Calogero-Sutherland model (CSM) is an integrable extension of the ordinary A-type CSM that possesses a reflection symmetry point. The BC-CSM is related to the chiral classes of random matrix ensembles (RMEs) in exactly the same…