Related papers: The WZW model on Random Regge Triangulations
We construct the Wess-Zumino-Witten (WZW) term in lattice gauge theory by using a Dirac operator which obeys the Ginsparg-Wilson relation. Topological properties of the WZW term known in the continuum are reproduced on the lattice as a…
We attempt to describe the moduli space of boundary states in the SU(2)$_k$ WZW model by constructing marginally deformed solutions in open string field theory in the level truncation approximation. In contrast with other approaches to…
A quantum group covariant extension of the chiral parts of the Wess-Zumino-Novikov-Witten model on a compact Lie group G gives rise to two matrix algebras with non-commutative entries. These are generated by "chiral zero modes" which…
We build two-dimensional quantum field theories on spin surfaces starting from theories on oriented surfaces with networks of topological defect lines and junctions. The construction uses a combinatorial description of the spin structure in…
Quantum geometry of twisted Wess--Zumino--Witten branes is formulated in the framework of twisted Reflection Equation Algebras. It is demonstrated how the representation theory of these algebras leads to the correct classification and…
Three-point functions of Wess-Zumino-Witten models are investigated. In particular, we study the level-dependence of three-point functions in the models based on algebras $su(3)$ and $su(4)$. We find a correspondence with…
We study branes and open strings in a large class of orbifolds of a curved background using microscopic techniques of boundary conformal field theory. In particular, we obtain factorizing operator product expansions of open string vertex…
Correlation functions of primary fields in the Wess-Zumino-Novikov-Witten (WZNW) model are known to satisfy a system of Knizhnik-Zamolodchikov (KZ) equations, which involve constants of motion of the exactly-solvable Gaudin magnet. We…
In this thesis we initiate a systematic study of branes in Wess-Zumino-Novikov-Witten models with Lie supergroup target space. We start by showing that a branes' worldvolume is a twisted superconjugacy class and construct the action of the…
WZW models are abstract conformal field theories with an infinite dimensional symmetry which accounts for their integrability, and at the same time they have a sigma model description of closed string propagation on group manifolds which,…
The Wigner $3j$ symbols of the quantum angular momentum theory are related to the vector coupling or Clebsch-Gordan coefficients and to the Hahn and dual Hahn polynomials of the discrete orthogonal hyperspherical family, of use in…
We study the Levin-Wen string-net model with a $Z_N$ type fusion algebra. Solutions of the local constraints of this model correspond to $Z_N$ gauge theory and double Chern-simons theories with quantum groups. For the first time, we…
We study fractional exclusion statistics for quantum systems with SU(2) symmetry (arbitrary spin $S$), by generalizing the thermodynamic equations with squeezed strings proposed by Ha and Haldane. The bare hole distributions as well as the…
This is a proceedings article reviewing a recent combinatorial construction of the su(n) WZNW fusion ring by C. Stroppel and the author. It contains one novel aspect: the explicit derivation of an algorithm for the computation of fusion…
We analyse the SU(2)_k WZNW models beyond the integrable representations and in particular the case of SU(2)_0. We find that these are good examples of logarithmic conformal field theories as indecomposable representations are naturally…
Gauged WZNW models are integrable conformal field theories. We integrate the classical \slu{} theory with periodic boundary conditions, which describes closed strings moving in a curved target-space geometry. We calculate its Poisson…
Global gauge symmetry becomes more intricate in low dimensional QFT. We survey the mathematical concepts leading to the relevant analogues of the (D=4) Doplicher-Haag-Roberts theory of superselection sectors and internal symmetry. We also…
We consider Hanany-Witten setups of 3- and 5-branes in type IIB string theory that realize N=(1,0),(2,0) and (1,1) gauged WZW models in 1+1 dimensions. The gauged WZW models arise as theories residing on the boundary of D3 branes ending on…
We invistigate exact solutions for the two-dimensional quantum field theories called Wess-Zumino-Novikov-Witten (WZNW) models. A WZNW model is a sigma model whose classical fields are applications from a bidimensional space-time (a Riemann…
A class of two-dimensional sigma models interpolating between $CP^1$ and the $SU(2)$ principal chiral model is discussed. We add the Wess-Zumino-Novikov-Witten term and examine the renormalization group flow of the two coupling constants…