相关论文: Lattice models from CFT on surfaces with holes II:…

We construct a one-parameter family of lattice models starting from a two-dimensional rational conformal field theory on a torus with a regular lattice of holes, each of which is equipped with a conformal boundary condition. The lattice…

We study integrable realizations of conformal twisted boundary conditions for sl(2) unitary minimal models on a torus. These conformal field theories are realized as the continuum scaling limit of critical G = A,D,E lattice models with…

I derive a formulation of the 2-dimensional critical Ising model on non-uniform simplicial lattices. Surprisingly, the derivation leads to a set of geometric constraints that a lattice must satisfy in order for the model to have a…

We demonstrate that the Ising model on a general triangular graph with 3 distinct couplings $K_1,K_2,K_3$ corresponds to an affine transformed conformal field theory (CFT). Full conformal invariance of the $c= 1/2$ minimal CFT is restored…

In this paper, we introduce a ``CFT factory'' : a novel algorithm of methodically generating 2D lattice models that would flow to 2D conformal fixed points in the infrared. These 2D models are realised by giving critical boundary conditions…

Non-compact Conformal Field Theories (CFTs) are central to several aspects of string theory and condensed matter physics. They are characterised, in particular, by the appearance of a continuum of conformal dimensions. Surprisingly, such…

We extend the recently introduced fuzzy sphere technique for the 3d Ising CFT to the case of boundary CFT (BCFT) using the fuzzy hemisphere. This allows to study conformal boundary conditions, and we investigate the three boundary…

In this work, we study unconventional anisotropic topologically ordered phases in $3d$ that manifest type-II fractonic physics along submanifolds. While they behave as usual topological order along a preferred spatial direction, their…

We study a relationship between conformally invariant boundary conditions and anomalies of conformal field theories (CFTs) in 1+1 dimensions. For a given CFT with a global symmetry, we consider symmetric gapping potentials which are…

Topological defect lines (TDLs) in two-dimensional conformal field theories (CFTs) are standard examples of generalized symmetries in quantum field theory. Integrable lattice incarnations of these TDLs, such as those provided by…

Critical statistical mechanics and Conformal Field Theory (CFT) are conjecturally connected since the seminal work of Beliavin, Polyakov, and Zamolodchikov [BPZ84a]. Both exhibit exactly solvable structures in two dimensions. A…

We set up a strategy for studying large families of logarithmic conformal field theories by using the enlarged symmetries and non--semi-simple associative algebras appearing in their lattice regularizations (as discussed in a companion…

It is shown that the partition function of the 2d Ising model on the dual finite lattice with periodical boundary conditions is expressed through some specific combination of the partition functions of the model on the torus with…

Topological/perfectly-transmissive defects play a fundamental role in the analysis of the symmetries of two dimensional conformal field theories (CFTs). In the present work, spin chain regularizations for these defects are proposed and…

Work of the last few years has shown that the key algebraic features of Logarithmic Conformal Field Theories (LCFTs) are already present in some finite lattice systems (such as the XXZ spin-1/2 chain) before the continuum limit is taken.…

We construct integrable realizations of conformal twisted boundary conditions for ^sl(2) unitary minimal models on a torus. These conformal field theories are realized as the continuum scaling limit of critical A-D-E lattice models with…

We construct (2+1)-dimensional lattice systems, which we call fusion surface models. These models have finite non-invertible symmetries described by general fusion 2-categories. Our method can be applied to build microscopic models with,…

Gapped phases in 2+1 dimensional quantum field theories with fusion 2-categorical symmetries were recently classified and characterized using the Symmetry Topological Field Theory (SymTFT) approach arXiv:2408.05266, arXiv:2502.20440. In…

This is the second in a series of three articles about recovering the full algebraic structure of a boundary conformal field theory (CFT) from the scaling limit of the critical Ising model in slit-strip geometry. Here we study the fusion…

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…