Related papers: Fermionic CFTs and classifying algebras

This chapter is an introduction to the Free Fermionic Formulation of String Theory, with emphasis on heterotic model building. After a brief review of bosonization in two dimensional conformal field theories, we discuss how internal bosonic…

We formulate a $\mathbb{Z}_k$-parafermionization/bosonization scheme for one-dimensional lattice models and field theories on a torus, starting from a generalized Jordan-Wigner transformation on a lattice, which extends the Majorana-Ising…

We present details of the phase diagrams of fermionic systems with random and frustrated interactions, emphasizing the important role of the chemical potential. The insulating fermionic Ising spin glass model is shown to reveal different…

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 formulate a family of spin Topological Quantum Filed Theories (spin-TQFTs) as fermionic generalization of bosonic Dijkgraaf-Witten TQFTs. They are obtained by gauging $G$-equivariant invertible spin-TQFTs, or, in physics language,…

This article aims to review a selection of central topics and examples in logarithmic conformal field theory. It begins with a pure Virasoro example, critical percolation, then continues with a detailed exposition of symplectic fermions,…

We introduce regular series expansion for weakly- and moderately-correlated fermionic systems, based on Fluctuating Local Field approach. The method relies on the explicit account of leading fluctuating mode(s) and is therefore suitable for…

A fermionic supersymmetric extension is established for the Gauss-Weingarten and Gauss-Codazzi equations describing conformally parametrized surfaces immersed in a Grassmann superspace. An analysis of this extension is performed using a…

We study the large-charge sector of large-N fermionic CFTs in three dimensions. Depending on the model and the nature of the fixed charge, we find two types of descriptions: in terms of a superfluid or a Fermi sphere. We explicitly compute…

We propose a novel approach to study conformal field theories (CFTs) in general dimensions. In the conformal bootstrap program, one usually searches for consistent CFT data that satisfy crossing symmetry. In the new approach, we reverse the…

We explain how to incorporate the action of local integrals of motion into the fermionic basis for the sine-Gordon model and its UV CFT. The examples up to the level 4 are presented. Numerical computation support the results. Possible…

We continue the program of bulk reconstruction for fermionic fields. We reconstruct, from the CFT, the Dirac fermion field in $AdS_{3}$ coupled to a Chern-Simon gauge field. We show that the three conditions; solving the equation of motion,…

We review various aspects of two dimensional conformal field theories paying close attention to the algebraic structures that intervene. We provide a compact description regarding the appearance of a chiral algebra as the symmetry algebra…

We construct a class of chiral fermionic CFTs from classical codes over finite fields whose order is a prime number. We exploit the relationship between classical codes and Euclidean lattices to provide the Neveu-Schwarz sector of fermionic…

This thesis examines the correspondence between models of statistical physics and Feynman graphs of quantum field theories (QFTs) by a common property: integrability. We review integrable structures for periodic boundary conditions on both…

Conformal invariance often accompanies criticality in Hermitian systems. However, its fate in non-Hermitian settings is less clear, especially near exceptional points where the Hamiltonian becomes non-diagonalizable. Here we investigate…

Motivated by the three-dimensional topological field theory / two-dimensional conformal field theory (CFT) correspondence, we study a broad class of one-dimensional quantum mechanical models, known as anyonic chains, that can give rise to…

We study the critical Ising model on the square lattice in bounded simply connected domains with + and free boundary conditions. We relate the energy density of the model to a fermionic observable and compute its scaling limit by discrete…

We introduce a finite-dimensional algebra that controls the possible boundary conditions of a conformal field theory. For theories that are obtained by modding out a Z_2 symmetry (corresponding to a so-called D_odd-type, or half-integer…

We propose a manifestly supersymmetric formulation of the Symmetry Topological Field Theory (SuSymTFT) for theories with supersymmetry. The SymTFT is a framework that helps organizing symmetries and anomalies of a QFT. Albeit a lot of…