Related papers: Verlinde lines, anyon permutations and commutant p…
We extend the TFT construction of CFT correlators of [arXiv:hep-th/0204148] to so-called finite logarithmic CFTs for which the algebraic input data is no longer semisimple but still finite. More specifically, starting from the data of a…
We investigate crosscap states in two-dimensional rational conformal field theories (RCFTs), with an emphasis on the role of non-invertible symmetries. In particular, we argue for the existence of crosscap states labelled by each Verlinde…
We study (generalized) discrete symmetries of 2d semisimple TQFTs. These are 2d TQFTs whose fusion rules can be diagonalized. We show that, in this special basis, the 0-form symmetries always act as permutations while 1-form symmetries act…
Conformal field theory (CFT) plays a key role in modern theoretical physics. Through CFT we describe real physical systems at criticality and fixed points of the renormalization group flow. It is also central in the study of quantum…
We use the Virasoro TQFT to derive an integral identity that we view as a non-rational generalization of the Verlinde formula for the Virasoro algebra with central charge $c\geq 25$. The identity expresses the Virasoro fusion kernel as an…
We study modular properties of the AdS3 WZNW model. Although the Euclidean partition function is modular invariant, the characters on the Euclidean torus are ill-defined and their modular transformations are unknown. We reconsider the…
Scalar-fermion models, such as the Gross-Neveu-Yukawa model, admit natural $1d$ defects given by the exponential of a scalar field integrated along a straight line. In $4-\varepsilon$ dimensions the defect coupling is weakly relevant and…
We consider topological defect lines (TDLs) in two-dimensional fermionic conformal field theories (CFTs). Besides inheriting all the properties of TDLs in bosonic CFTs, TDLs in fermionic CFTs could host fermionic defect operators at their…
The interpretation of D-branes in terms of open strings has lead to much interest in boundary conditions of two-dimensional conformal field theories (CFTs). These studies have deepened our understanding of CFT and allowed us to develop new…
We study gapped boundaries characterized by "fermionic condensates" in 2+1 d topological order. Mathematically, each of these condensates can be described by a super commutative Frobenius algebra. We systematically obtain the species of…
The critical 2d classical Ising model on the square lattice has two topological conformal defects: the $\mathbb{Z}_2$ symmetry defect $D_{\epsilon}$ and the Kramers-Wannier duality defect $D_{\sigma}$. These two defects implement…
Error-correcting codes are known to define chiral 2d lattice CFTs where all the $U(1)$ symmetries are enhanced to $SU(2)$. In this paper, we extend this construction to a broader class of length-$n$ codes which define full (non-chiral) CFTs…
An account is given of the structure and representations of chiral bosonic meromorphic conformal field theories (CFT's), and, in particular, the conditions under which such a CFT may be extended by a representation to form a new theory.…
We study conformal field theories (CFTs) on curved spaces including both orientable and unorientable manifolds possibly with boundaries. We first review conformal transformations on curved manifolds. We then compute the identity components…
We consider topological defect lines (TDLs) in two-dimensional conformal field theories. Generalizing and encompassing both global symmetries and Verlinde lines, TDLs together with their attached defect operators provide models of fusion…
Starting from an abelian rigid braided monoidal category C we define an abelian rigid monoidal category C_F which captures some aspects of perturbed conformal defects in two-dimensional conformal field theory. Namely, for V a rational…
We study whether the relations between the Weyl anomaly, entanglement entropy (EE), and thermal entropy of a two-dimensional (2D) conformal field theory (CFT) extend to 2D boundaries of 3D CFTs, or 2D defects of $D \geq 3$ CFTs. The Weyl…
We extend the Mellin representation of conformal field theory (CFT) to allow for conformal boundaries and interfaces. We consider the simplest holographic setup dual to an interface CFT - a brane filling an $AdS_{d}$ subspace of $AdS_{d+1}$…
We extend our previous work arXiv:1012.5721 [hep-th] on the non-compact N=2 SCFT_2 defined as the supersymmetric SL(2,R)/U(1)-gauged WZW model. Starting from path-integral calculations of torus partition functions of both the axial-type…
It is well understood that 2d conformal field theory (CFT) deformed by an irrelevant $T\bar{T}$ perturbation of dimension $4$ has universal properties. In particular, for the most interesting cases, the theory develops a singularity in the…