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Related papers: 2d Conformal Field Theories on Magic Triangle

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Wess-Zumino-Witten (WZW) models are among the most basic and most studied Conformal Field Theories (CFT). They have had a huge influence not only in physics but also in mathematics, in representation theory and geometry. However their…

Mathematical Physics · Physics 2025-02-25 Colin Guillarmou , Antti Kupiainen , Rémi Rhodes

We present some new results on the rational solutions of the Knizhnik-Zamolodchikov equation for the four-point conformal blocks of isospin I primary fields in the SU(2)_k Wess-Zumino-Novikov-Witten model. The rational solutions…

High Energy Physics - Theory · Physics 2009-11-07 Ludmil Hadjiivanov , Todor Popov

It is known that there are 48 Virasoro algebras acting on the monster conformal field theory. We call conformal field theories with such a property, which are not necessarily chiral, code conformal field theories. In this paper, we…

Quantum Algebra · Mathematics 2021-09-15 Yuto Moriwaki

Rational conformal field theories produce a tower of finite-dimensional representations of surface mapping class groups, acting on the conformal blocks of the theory. We review this formalism. We show that many recent mathematical…

Quantum Algebra · Mathematics 2007-10-09 T. Gannon

Introduction to two dimensional conformal field theory on open and unoriented surfaces. The construction is illustrated in detail on the example of SU(2) WZW models.

High Energy Physics - Theory · Physics 2007-05-23 Yassen S. Stanev

The massive soliton theories describe integrable perturbations of WZW cosets as generalized multi-component sine-Gordon models. We study their coupling to 2-dim gravity in the conformal gauge and show that the resulting models can be…

High Energy Physics - Theory · Physics 2009-10-30 Ioannis Bakas , Q-Han Park

Limits of families of conformal field theories are of interest in the context of AdS/CFT dualities. We explore here the large level limit of the two-dimensional N=(2,2) superconformal W_{n+1} minimal models that appear in the context of the…

High Energy Physics - Theory · Physics 2014-08-05 Stefan Fredenhagen , Cosimo Restuccia

We introduce a general theory of homological Milnor-Witt cycle modules over an excellent base scheme equipped with a dimension function, extending both Rost's cycle modules and Feld's theory over fields. To any such module we associate a…

Algebraic Geometry · Mathematics 2025-12-11 Frédéric Déglise , Niels Feld , Fangzhou Jin

The goal of these notes is to give a brief explanation of how electric-magnetic duality in four dimensions is related to the existence of an unusual conformal field theory in six dimensions.

Representation Theory · Mathematics 2008-02-07 Edward Witten

We generalize, to any space-time dimension, the unitarity bounds of highest weight UIR's of the conformal groups with Lie algebras $so(2,d)$. We classify gauge theories invariant under $so(2,d)$, both integral and half-integral spins. A…

High Energy Physics - Theory · Physics 2016-09-06 S. Ferrara , C. Fronsdal

The singular part of the \textit{operator product expansion} (OPE) of a pair of \textit{globally conformal invariant} (GCI) scalar fields $\phi$ of (integer) dimension $d$ can be written as a sum of the 2-point function of $\phi$ and $d-1$…

High Energy Physics - Theory · Physics 2007-05-23 Nikolay M. Nikolov , Yassen S. Stanev , Ivan T. Todorov

Monoidal categories with additional structure such as a braiding or some form of duality abound in quantum topology. They often appear in tandem with Frobenius algebras inside them. Motivations for this range from the theory of module…

Quantum Algebra · Mathematics 2025-07-23 Lukas Woike

We study a homogeneous system of $d+8$ linear partial differential equations (PDEs) in $d$ variables arising from two-dimensional Conformal Field Theories (CFTs) with a $W_3$-symmetry algebra. In the CFT context, $d$ PDEs are third-order…

Mathematical Physics · Physics 2025-08-21 Augustin Lafay , Ian Le , Julien Roussillon

Conformal field theory finds applications across diverse fields, from statistical systems at criticality to quantum gravity through the AdS/CFT correspondence. These theories are subject to strong constraints, enabling a systematic…

High Energy Physics - Theory · Physics 2024-01-22 Julien Barrat

We study conformal field theory in $d=1$ space-time dimensions. We derive a dispersion relation for the 4-point correlation function of identical bosons and fermions, in terms of the double discontinuity. This extends the conformal…

High Energy Physics - Theory · Physics 2025-01-10 Dean Carmi , Sudip Ghosh , Trakshu Sharma

Schramm-Loewner evolution (SLE) is a random process that gives a useful description of fractal curves. After its introduction, many works concerning the connection between SLE and conformal field theory (CFT) have been carried out. In this…

Mathematical Physics · Physics 2019-06-26 Shinji Koshida

Using a Hamiltonian approach to gauged WZW models, we present a general method for computing the conformally exact metric and dilaton, to all orders in the $1/k$ expansion, for any bosonic, heterotic, or type-II superstring model based on a…

High Energy Physics - Theory · Physics 2013-11-13 I. Bars , K. Sfetsos

We examine the correspondence between the conformal field theory of boundary operators and two-dimensional hyperbolic geometry. By consideration of domain boundaries in two-dimensional critical systems, and the invariance of the hyperbolic…

High Energy Physics - Theory · Physics 2009-10-22 P. Kleban , I. Vassileva

We introduce and study completely-extendable conformal intertwining algebras. Based on results obtained in other papers, various examples are given. Duals of these algebras are constructed and nondegenerate such algebras are defined. We…

Quantum Algebra · Mathematics 2007-05-23 Yi-Zhi Huang

We relate duality mappings to the "Babbage equation" F(F(z)) = z, with F a map linking weak- to strong-coupling theories. Under fairly general conditions F may only be a specific conformal transformation of the fractional linear type. This…

Statistical Mechanics · Physics 2015-01-08 Zohar Nussinov , Gerardo Ortiz , Mohammad-Sadegh Vaezi