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We have shown that a particular class of non-local free field theory has conformal symmetry in arbitrary dimensions. Using the local field theory counterpart of this class, we have found the Noether currents and Ward identities of the…
We review some results concerning the properties of static, spherically symmetric solutions of multidimensional theories of gravity: various scalar-tensor theories and a generalized string-motivated model with multiple scalar fields and…
In this paper we derive the scaling fields in $c=-2$ conformal field theory associated with weakly allowed clusters in abelian sandpile model and show a direct relation between the two models.
Conformal blocks form a system of vector bundles over the moduli space of complex curves with marked points. We discuss various aspects of these bundles. In particular, we present conjectures about the dimensions of sub-bundles. They imply…
Two-dimensional conformal field theory (CFT) can be defined through its correlation functions. These must satisfy certain consistency conditions which arise from the cutting of world sheets along circles or intervals. The construction of a…
A solution to the long-standing problem of identifying the conformal field theory governing the transition between quantized Hall plateaus of a disordered noninteracting 2d electron gas, is proposed. The theory is a nonlinear sigma model…
We introduce a finite-dimensional algebra that controls the possible boundary conditions of a conformal field theory. For theories that are obtained by modding out a Z_2 symmetry (corresponding to a so-called D_odd-type, or half-integer…
We review various aspects of two dimensional conformal field theories paying close attention to the algebraic structures that intervene. We provide a compact description regarding the appearance of a chiral algebra as the symmetry algebra…
We review how modular categories, and commutative and non-commutative Frobenius algebras arise in rational conformal field theory. For Euclidean CFT we use an approach based on sewing of surfaces, and in the Minkowskian case we describe CFT…
For decades, a lot of work has been devoted to the problem of constructing a non-trivial quantum field theory in four-dimensional space time. This letter addresses the attempts to construct an algebraic quantum field theory in the framework…
This is an invited contribution to the 2nd edition of the Encyclopedia of Mathematical Physics. We review the following algebraic structures which appear in two-dimensional conformal field theory (CFT): The symmetries of two-dimensional…
Affine Kac-Moody algebras give rise to interesting systems of differential equations, so-called Knizhnik-Zamolodchikov equations. The monodromy properties of their solutions can be encoded in the structure of a modular tensor category on (a…
The trace anomaly for a conformally invariant scalar field theory on a curved manifold of positive constant curvature with boundary is considered. In the context of a perturbative evaluation of the theory's effective action explicit…
For some time now, conformal field theories in two dimensions have been studied as integrable systems. Much of the success of these studies is related to the existence of an operator algebra of the theory. In this paper, some of the…
We discuss the infinite dimensional algebras appearing in integrable perturbations of conformally invariant theories, with special emphasis in the structure of the consequent non-abelian infinite dimensional algebra generalizing $W_\infty$…
This is a set of lecture notes on the operator algebraic approach to 2-dimensional conformal field theory. Representation theoretic aspects and connections to vertex operator algebras are emphasized. No knowledge on operator algebras or…
We study circuit complexity for conformal field theory states in arbitrary dimensions. Our circuits start from a primary state and move along a unitary representation of the Lorentzian conformal group. Different choices of distance…
A class of two-dimensional globally scale-invariant, but not conformally invariant, theories is obtained. These systems are identified in the process of discussing global and local scaling properties of models related by duality…
The local logarithmic conformal field theory corresponding to the triplet algebra at c=-2 is constructed. The constraints of locality and crossing symmetry are explored in detail, and a consistent set of amplitudes is found. The spectrum of…
We study conformal field theory on two-dimensional orbifolds and show this to be an effective way to analyze physical effects of geometric singularities with angular deficits. They are closely related to boundaries and cross caps.…