Related papers: Fermionic CFTs and classifying algebras
We study the Abelian Thirring Model when the fermionic fields have non-conserved chiral charge: $\Delta {\cal Q}_5 =N$. One of the main features we find for this model is the dependence of the Virasoro central charge on both the Thirring…
Chiral edge states of 2+1 dimensional Abelian and non-Abelian topological phases can be represented by chiral conformal field theories with integer and non-integer values of central charge, respectively. In this work we describe certain…
These lectures consisted of an elementary introduction to conformal field theory, with some applications to statistical mechanical systems, and fewer to string theory. Contents: 1. Conformal theories in d dimensions 2. Conformal theories in…
This work proposes a minimal model extending the duality between classical statistical spin systems and fermionic systems beyond the case of free fermions. A Jordan-Wigner transformation applied to a two-dimensional tensor network maps the…
The M$_k$ models for 1D lattice fermions are characterised by ${\cal N}=2$ supersymmetry and by an order-$k$ clustering property. This paper highlights connections with quantum field theories (QFTs) in various regimes. At criticality the…
We provide a classification of invertible topological phases of interacting fermions with symmetry in two spatial dimensions for general fermionic symmetry groups $G_f$ and general values of the chiral central charge $c_-$. Here $G_f$ is a…
Using results on topological band theory of phases of matter and discrete symmetries, we study topological properties of band structure of physical systems involving spin $\frac{1}{2}$ and $\frac{3}{2}$ fermions. We apply this approach to…
The Casimir force between two perfectly reflecting parallel plates is considered. In a recent paper we presented generalised physical boundary conditions describing perfectly reflecting parallel plates. These boundary conditions are…
We study operators with large internal charge in boundary conformal field theories (BCFTs) with internal symmetries. Using the state-operator correspondence and the existence of a macroscopic limit, we find a non-trivial relation between…
We prove convergence of the 2- and 4-point fermionic observables of the FK-Ising model on simply connected domains discretised by a planar isoradial lattice in massive (near-critical) scaling limit. The former is alternatively known as a…
In this dissertation, we present work towards characterizing various conformal and nearly conformal quantum field theories nonperturbatively using a combination of numerical and analytical techniques. A key area of interest is the conformal…
The operator algebra of fermionic modes is isomorphic to that of qubits, the difference between them is twofold: the embedding of subalgebras corresponding to mode subsets and multiqubit subsystems on the one hand, and the parity…
A family of multispecies Ising models on generalized regular random graphs is investigated in the thermodynamic limit. The architecture is specified by class-dependent couplings and magnetic fields. We prove that the magnetizations,…
Conformal interfaces separating two conformal field theories (CFTs) provide maps between different CFTs, and naturally exist in nature as domain walls between different phases. One particularly interesting construction of a conformal…
We present fermionic sum representation for the general Virasoro character of the unitary minimal superconformal series ($N=1$). Example of the corresponding ``finitizated" identities relating corner transfer matrix polynomials with…
We derive new finitized fermionic characters for the superconformal unitary minimal models by interpreting the RSOS configuration sums as fermi-gas partition functions. This extends to the supersymmetric case the method introduced by…
We study the conformal bootstrap in fractional space-time dimensions, obtaining rigorous bounds on operator dimensions. Our results show strong evidence that there is a family of unitary CFTs connecting the 2D Ising model, the 3D Ising…
We consider interfaces between critical spin-chains in different universality classes, described in the continuum limit by defect/interface conformal field theory (DCFT/ICFT). We find a new conformal interface between the Tricritical Ising…
We continue the construction of a Lagrangian description of irreducible half-integer higher-spin representations of the Poincare group with an arbitrary Young tableaux having $k$ rows, on a basis of the BRST--BFV approach suggested for…
In this paper and its sequel, we construct topologically invariant defects in two-dimensional classical lattice models and quantum spin chains. We show how defect lines commute with the transfer matrix/Hamiltonian when they obey the defect…