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We construct generalized symmetries in two-dimensional symmetric product orbifold CFTs $\text{Sym}^N(\mathcal{T}),$ for a generic seed CFT $\mathcal{T}$. These symmetries are more general than the universal and maximally symmetric ones…
We introduce the AdS/CFT correspondence as a natural extension of QFT in a fixed AdS background. We start by reviewing some general concepts of CFT, including the embedding space formalism. We then consider QFT in a fixed AdS background and…
This lecture note covers topics on boundary conformal field theory, modular transformations and the Verlinde formula, and boundary logarithmic CFT. An introductory review on CFT with boundary and a discussion of its applications to…
It is well-known that classical two-dimensional topological field theories are in one-to-one correspondence with commutative Frobenius algebras. An important extension of classical two-dimensional topological field theories is provided by…
Invariants of 3-manifolds from a non semi-simple category of modules over a version of quantum $sl(2)$ were obtained by the last three authors in arXiv:1202.3553 . They are invariants of $3$-manifolds together with a cohomology class which…
We revisit the problem of bootstrapping CFT correlators of charged fields. After discussing in detail how bounds for uncharged fields can be recycled to the charged case, we introduce two sets of analytic functional bases for correlators on…
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…
In conformal field theory the understanding of correlation functions can be divided into two distinct conceptual levels: The analytic properties of the correlators endow the representation categories of the underlying chiral symmetry…
This is a combined review on the Kerr/CFT correspondence on the one hand and solvable irrelevant deformations of two-dimensional QFTs - specifically, the $T\bar T$ and $J\bar T$ deformations - on the other. These subjects are…
Conformal field theories (CFTs) with cubic global symmetry in 3D are relevant in a variety of condensed matter systems and have been studied extensively with the use of perturbative methods like the $\varepsilon$ expansion. In an earlier…
A concise review of the notions of elliptic functions, modular forms, and theta-functions is provided, devoting most of the paper to applications to Conformal Field Theory (CFT), introduced within the axiomatic framework of quantum field…
Conformal field theory (CFT) has become an active area of research beyond its origins in statistical physics and attracted much attention due to its intrinsic mathematical interest, which reveals deep connections with other diverse branches…
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…
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…
The Lorentzian AdS/CFT correspondence implies a map between local operators in supergravity and non-local operators in the CFT. By explicit computation we construct CFT operators which are dual to local bulk fields in the semiclassical…
We analyze the concomitant spontaneous breaking of translation and conformal symmetries by introducing in a CFT a complex scalar operator that acquires a spatially dependent expectation value. The model, inspired by the holographic…
We study the map between two descriptions of the $T\bar{T}$ deformation of conformal field theory (CFT): One is the defining description as a deformation of CFT by the $T\bar{T}$-operator. The other is an alternative description as the…
We begin by reexamining the holographic reconstruction of scalar fields in four-dimensional anti-de Sitter spacetime, adopting a purely Lorentzian signature derivation, reproducing earlier results of HKLL and generalizing to arbitrary…
We use factorizable finite tensor categories, and specifically the representation categories of factorizable ribbon Hopf algebras H, as a laboratory for exploring bulk correlation functions in local logarithmic conformal field theories. For…
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…