Related papers: Hidden Grassmann Structure in the XXZ Model IV: CF…
Strongly interacting models often possess "dualities" subtler than a one-to-one mapping of energy levels. The maps can be non-invertible, as apparent in the canonical example of Kramers and Wannier. We analyse an algebraic structure common…
We investigate and characterize the dynamics of operator growth in irrational two-dimensional conformal field theories. By employing the oscillator realization of the Virasoro algebra and CFT states, we systematically implement the Lanczos…
It is demonstrated that several series of conformal field theories, while satisfying braid group statistics, can still be described in the conventional setting of the DHR theory, i.e. their superselection structure can be understood in…
In this article, we provide a detailed construction and analysis of the mathematical conformal field theory of the free fermion, defined in the sense of Graeme Segal. We verify directly that the operators assigned to disks with two disks…
Transition rates and dynamic spin structure factor at zero temperature for the spin-1/2 XXZ chain at critical regime in a magnetic field are numerically evaluated in terms of the exact determinant representations for the form factors and…
We formulate and discuss a number of conjectures on the ground state vectors of the XYZ-spin chains of odd length with periodic boundary conditions and a special choice of the Hamiltonian parameters. In particular, arguments for the…
We systematically study how the integrality of the conformal characters shapes the space of fermionic rational conformal field theories in two dimensions. The integrality suggests that conformal characters on torus with a given choice of…
In this paper we analyze the classical XXZ spin chain with reflecting boundaries. We exhibit a system of log-canonical coordinates on the phase space generalizing Sklyanin's separation of variables for the periodic XXZ chain, and use these…
We consider limit sets of some conformal iterated function systems, and introduce classes of subsets of the limit set, with the property that the classes are closed under countable intersections and all sets in the classes have large…
We consider three dimensional conformal field theories that have a higher spin symmetry that is slightly broken. The theories have a large N limit, in the sense that the operators separate into single trace and multitrace and obey the usual…
It is known that there are 48 Virasoro algebras acting on the monster conformal field theory. We call conformal field theories with such a property, which are not necessarily chiral, code conformal field theories. In this paper, we…
The goal of this paper is to define fermionic fields on causal set. This is done by the use of holonomies to define vierbines, and then defining spinor fields by taking advantage of the leftover degrees of freedom of holonomies plus…
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…
Three aspects of symmetry structure of lattice chiral fermion in the overlap formalism are discussed. By the weak coupling expansion of the overlap Dirac operator, the axial anomaly associated to the chiral transformation proposed by…
Warped conformal field theories (WCFTs) are two-dimensional non-relativistic systems, with a chiral scaling and shift symmetry. We present a detailed derivation of the near-extremal limit for their torus partition function. This limit…
We introduce a transformation which allows the fermionization of operators of any one-dimensional spin-chain. This fermionization procedure is independent of any eventual integrable structure and is compatible with it. We illustrate this…
We propose a variational method for identifying lattice operators in a critical quantum spin chain with scaling operators in the underlying conformal field theory (CFT). In particular, this allows us to build a lattice version of the…
We apply the method of the large spin bootstrap to analyse fermionic conformal field theories with weakly broken higher spin symmetry. Through the study of correlators of composite operators, we find the anomalous dimensions and OPE…
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…
Warped conformal field theories in two dimensions are exotic nonlocal, Lorentz violating field theories characterized by Virasoro-Kac-Moody symmetries and have attracted a lot of attention as candidate boundary duals to warped AdS$_3$…