Related papers: Conformal Field Theory in D>2 dimensions, represen…
The simplest possible noncommutative harmonic oscillator in two dimensions is used to quantize the free closed bosonic string in two flat dimensions. The partition function is not deformed by the introduction of noncommutativity, if we…
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…
We study a statistical model defined by a conformally invariant distribution of overlapping spheres in arbitrary dimension d. The model arises as the asymptotic distribution of cosmic bubbles in d+1 dimensional de Sitter space, and also as…
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.…
We consider representations of meromorphic bosonic chiral conformal field theories, and demonstrate that such a representation is completely specified by a state within the theory. The necessary and sufficient conditions upon this state are…
The theory of a massless two-dimensional scalar field with a periodic boundary interaction is considered. At a critical value of the period this system defines a conformal field theory and can be re-expressed in terms of free fermions,…
We summarize recent progress in the understanding of fixed point resolution for conformal field theories. Fixed points in both coset conformal field theories and non-diagonal modular invariants which describe simple current extensions of…
Based upon the formalism of conformal field theory with a boundary, we give a description of the boundary effect on fully developed two dimensional turbulence. Exact one and two point velocity correlation functions and energy power spectrum…
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…
We derive a generating function for all the 3-point functions of higher spin conserved currents in four dimensional conformal field theory. The resulting expressions have a rather surprising factorized form which suggest that they can all…
We review a formalism of superstring quantization with manifest six-dimensional spacetime supersymmetry, and apply it to AdS_3 x S^3 backgrounds with Ramond-Ramond flux. The resulting description is a conformal field theory based on a sigma…
Any four-dimensional $\mathcal{N} \geqslant 2$ superconformal field theory possess a protected subsector isomorphic to a two-dimensional chiral algebra \cite{Beem:2013sza}. The goal of these lectures is to provide an introduction to the…
This is the second part of the paper 0709.3806v2. Here we show that three-point correlation function with one semi-degenerate field in Toda field theory as well as four-point correlation function with one completely degenerate and one…
Representations of four-dimensional superconformal groups on harmonic superfields are discussed. It is shown how various short representations can be obtained by parabolic induction. It is also shown that such short multiplets may admit…
In this article we inspect the dynamics of classical field theories with a local conformal behavior. Our interest in the multisymplectic setting comes from its suitable description of field theories, and the conformal character has been…
In the following few pages an account is given of a theme, which I began in 1966 and followed to the present.
It is argued that chiral algebras of conformal field theory possess a W-algebra structure. A survey of explicitly known W-algebras and their constructions is given. (Talk given at the XIX International Colloquium on ``Group Theoretical…
We define transformation of multiplets of fields (Jordan cells) under the D-dimensional conformal group, and calculate two and three point functions of fields, which show logarithmic behaviour. We also show how by a formal differentiation…
I discuss some aspects of conformal defects and conformal interfaces in two spacetime dimensions. Special emphasis is placed on their role as spectrum-generating symmetries of classical string theory.
It is shown that time-ordered correlation functions of a unitary CFT$_2$ in 2D Minkowski space admit a single-valued, conformally-invariant extension to the Lorentzian signature torus provided that the $S^1\times S^1$ spatial and temporal…