Related papers: SU(2) WZW Theory at Higher Genera
The Wess-Zumino-Witten model defined on the group SU(2) has a unique (non-trivial) simple current of conformal dimension k/4 for each level k. The extended algebra defined by this simple current is carefully constructed in terms of…
We study field theories defined in regions of the spatial non-commutative (NC) plane with a boundary present delimiting them, concentrating in particular on the U(1) NC Chern-Simons theory on the upper half plane. We find that classical…
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…
The purpose of this paper is to study categorifications of tensor products of finite dimensional modules for the quantum group for sl(2). The main categorification is obtained using certain Harish-Chandra bimodules for the complex Lie…
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…
The $GL(1|1)$ WZW model in the free field realization that uses the $bc$ system is revisited. By bosonizing the $bc$ system we describe the Neveu--Schwarz and Ramond sector modules $\mathcal V^{\text{NS}}_{en}=\bigoplus_{l\in\mathbb…
We introduce a simple method to extract the representation content of the spectrum of a system with SU(2) symmetry from its partition function. The method is easily generalized to systems with SO(2,4) symmetry, such as conformal field…
By using the Dyson-Schwinger/Bethe-Salpeter formalism in Euclidean spacetime, we calculate the ground state spectrum of $J\leq 1$ hadrons in an SU(2) gauge theory with 2 fundamental fermions. We show that the rainbow-ladder truncation,…
We study generating functions for the scalar products of SU(2) coherent intertwiners, which can be interpreted as coherent spin network evaluations on a 2-vertex graph. We show that these generating functions are exactly summable for…
We study a matrix model obtained by dimensionally reducing Chern-Simon theory on S^3. We find that the matrix integration is decomposed into sectors classified by the representation of SU(2). We show that the N-block sectors reproduce SU(N)…
For the case of the SU(2) WZW model at level one, the boundary states that only preserve the conformal symmetry are analysed. Under the assumption that the usual Cardy boundary states as well as their marginal deformations are consistent,…
Recently we suggested a new quantum algebra, the moduli algebra, which was conjectured to be a quantum algebra of observables of the Hamiltonian Chern Simons theory. This algebra provides the quantization of the algebra of functions on the…
Higher dimensional Chern-Simons theories, even though constructed along the same topological pattern as in 2+1 dimensions, have been shown recently to have generically a non-vanishing number of degrees of freedom. In this paper, we carry…
We perform a dimensional reduction of the $U(1)\times SU(2)$ Chern--Simons bosonization and apply it to the $t-J$ model, relevant for high $T_c$ superconductors. This procedure yields a decomposition of the electron field into a product of…
We analyze boundary states in the SU(2)$_k$ WZW model using open string field theory in the level truncation approximation. We develop algorithms that allow effective calculation of action in this model and we search for classical solutions…
According to the work of Berkovits, Vafa and Witten (hep-th/9902098), the non-linear sigma model on the supergroup PSU(1,1|2) is the essential building block for string theory on AdS(3)xS(3)xT(4). Models associated with a non-vanishing…
The Wess-Zumino term in two-dimensional conformal field theory is best understood as a surface holonomy of a bundle gerbe. We define additional structure for a bundle gerbe that allows to extend the notion of surface holonomy to unoriented…
A systematic description of the Wess-Zumino-Witten model is presented. The symplectic method plays the major role in this paper and also gives the relationship between the WZW model and the Chern-Simons model. The quantum theory is obtained…
The Witten index counts the difference in the number of bosonic and fermionic states of a quantum mechanical system. The Schur index, which can be defined for theories with at least $\mathcal{N}=2$ supersymmetry in four dimensions is a…
We study $U(1) \times U(1) \rtimes Z_2$ Chern-Simons theory with integral coupling constants (k,l) and its relation to certain non-Abelian fractional quantum Hall (FQH) states. For the $U(1) \times U(1) \rtimes Z_2$ Chern-Simons theory, we…