Related papers: The FZZ-Duality Conjecture - A Proof

For two distinct primes p and l, we investigate the Z_l-cohomology of the Lubin-Tate towers of a p-adic field. We prove that it realizes some version of Langlands and Jacquet-Langlands correspondences for flat families of irreducible…

We construct dual descriptions of (0,2) gauged linear sigma models. In some cases, the dual is a (0,2) Landau-Ginzburg theory, while in other cases, it is a non-linear sigma model. The duality map defines an analogue of mirror symmetry for…

We discuss non-compact WZW sigma models, especially the ones with symmetric space $H^{\bf C}/H$ as the target, for $H$ a compact Lie group. They offer examples of non-rational conformal field theories. We remind their relation to the…

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…

We formulate two-dimensional rational conformal field theory as a natural generalization of two-dimensional lattice topological field theory. To this end we lift various structures from complex vector spaces to modular tensor categories.…

We construct a "Koszul duality" equivalence relating the (diagrammatic) Hecke category attached to a Coxeter system and a given realization to the Hecke category attached to the same Coxeter system and the dual realization. This extends a…

A recently proposed correspondence between 4-dimensional N=2 SUSY SU(k) gauge theories on R^4/Z_m and SU(k) Toda-like theories with Z_m parafermionic symmetry is used to construct four-point N=1 super Liouville conformal block, which…

Recently Alday, Gaiotto and Tachikawa have proposed relation between 2- and 4-dimensional conformal field theories. The relation implies that the Nekrasov partition functions of N=2 superconformal gauge theories are equal to conformal…

Liouville field theory is considered with boundary conditions corresponding to a quantization of the classical Lobachevskiy plane (i.e. euclidean version of $AdS_2$). We solve the bootstrap equations for the out-vacuum wave function and…

We consider a class of two dimensional conformal ${\mathcal N}=2$ supersymmetric $U(1)$ gauge linear sigma models with $N$ fields of charges $+1$ and $N$ fields of charges $-1$, whose Higgs branches are non-compact toric Calabi-Yau…

We reconsider the construction of exponential fields in the quantized Liouville theory. It is based on a free-field construction of a continuous family or chiral vertex operators. We derive the fusion and braid relations of the chiral…

Similarly to the bosonic Liouville theory, the $\mathcal{N}=2$ supersymmetric Liouville theory was conjectured to be equipped with the duality that exchanges the superpotential and the K\"ahler potential. The conjectured duality, however,…

For any complex simple Lie algebra, we generalize primary fileds in the Wess-Zumino-Novikov-Witten conformal field theory with respect to the case of irregular singularities and we construct integral representations of hypergeometric…

Motivated by a result from string topology, we prove a duality in topological Hochschild homology (THH). The duality relates the THH of an E_1-algebra spectrum and the THH of its derived Koszul dual algebra under certain compactness…

This is a very brief survey of some results in the geometry of string duality delivered at a lecture given at ICM 1998, Berlin. String Duality is the statement that one kind of string theory compactified on one space is equivalent in some…

This paper studies the analytic continuation of Liouville eigenstates and shows that they assemble into irreducible highest-weight representations of the Virasoro algebra, for all values of the conformal weights. This builds on previous…

$T\bar{T}$ deformed conformal field theories can be reformulated as worldsheet theories of non-critical strings. We use this correspondence to compute and study the $T\bar{T}$ deformed partition sum of a symmetric product CFT. We find that…

The study of the packing of a length of wire in a two dimensional domain is done using techniques of conformal maps. The resulting scaling properties are derived through the Coulomb gas formalism of Conformal Field Theories. An analogy is…

We generalize S-duality to N=2 superconformal field theories (SCFTs) with Coulomb branch operators of non-integer scaling dimension. As simple examples, we find minimal generalizations of the S-dualities discovered in SU(2) gauge theory…

In string theory it is known that abelian isometries in the sigma model lead to target space duality. We generalize this duality to backgrounds with non--abelian isometries. The procedure we follow consists of gauging the isometries of the…