Related papers: Conformal quantum field theory in various dimensio…
We propose a novel approach to study conformal field theories (CFTs) in general dimensions. In the conformal bootstrap program, one usually searches for consistent CFT data that satisfy crossing symmetry. In the new approach, we reverse the…
This paper is a collection of lecture notes on the superfield approach in three- and four-dimensional supersymmetric quantum field theory. Many examples of the applications of this approach to different superfield models are considered.
In this work, we study the supersymmetric warped conformal field theory in two dimensions. We show that the Hofman-Strominger theorem on symmetry enhancement could be generalized to the supersymmetric case. More precisely, we find that…
Every conformal field theory has the symmetry of taking each field to its adjoint. We consider here the quotient (orbifold) conformal field theory obtained by twisting with respect to this symmetry. A general method for computing such…
We investigate a one dimensional quantum mechanical model, which is invariant under translations and dilations but does not respect the conventional conformal invariance. We describe the possibility of modifying the conventional conformal…
A holographic conformal field theory is dual to semi-classical general relativity in Anti-de Sitter space coupled to matter fields. If the CFT factorizes in the large-$N$ limit, then all couplings in its dual are suppressed by the Planck…
I review three different problems occuring in two dimensional field theory: 1) classification of conformal field theories; 2) construction of lattice integrable realizations of the latter; 3) solutions to the WDVV equations of topological…
A straightforward relationship between the two approaches to 3-dimensional topological invariants, one of them put forward by Witten in the framework of topological quantum field theory, and the second one proposed by Kohno in terms of…
We review conformal field theory on the plane in the conformal bootstrap approach. We introduce the main ideas of the bootstrap approach to quantum field theory, and how they apply to two-dimensional theories with local conformal symmetry.…
Neural Network Field Theories (NN-FTs) represent a novel construction of arbitrary field theories, including those of conformal fields, through the specification of the network architecture and prior distribution for the network parameters.…
In the paper, the family of conformal four-point ladder diagrams in arbitrary space-time dimensions is considered. We use the representation obtained via explicit calculation using the operator approach and conformal quantum mechanics to…
The correspondence between quantum mechanics and noncommutative geometry is illustrated in the context of the noncommutative ${\rm AdS}^2_{\theta}/{\rm CFT_1}$ duality where ${\rm CFT}_1$ is identified as conformal quantum mechanics. This…
We consider logarithmic conformal field theories near a boundary and derive the general form of one and two point functions. We obtain results for arbitrary and two dimensions. Application to two dimensional magnetohydrodynamics is…
This is a philosophical paper. It claims that there is a gap to be filled in the relationship between complexity theory (CT) and quantum theory (QT). This gap concerns two very distinct understandings of time. The paper provides the ground…
The modern way to understand symmetries of a quantum field theory is via its topological defects in various dimensions. In this contribution to the proceedings we focus on line defects in 2d QFT and we point out that topological defects…
We summarize the results obtained in the last few years about permutation orbifolds in two-dimensional conformal field theories, their application to string theory and their use in the construction of four-dimensional heterotic string…
In many cases the symmetry structure of quantum field theories can be neatly encoded into their associated symmetry topological field theory (SymTFT), a topological field theory in one dimension higher. For geometrically engineered QFTs in…
Globally conformal invariant quantum field theories in a D-dimensional space-time (D even) have rational correlation functions and admit an infinite number of conserved (symmetric traceless) tensor currents. In a theory of a scalar field of…
V. Drinfeld proposed conjectures on geometric Langlands correspondence and its quantum deformation. We refine these conjectures and propose their relationship with algebraic conformal field theory.
Vertex algebras in higher dimensions correspond to models of quantum field theory with global conformal invariance. Any vertex algebra in dimension D admits a restriction to a vertex algebra in any lower dimension and, in particular, to…