Related papers: SU(2) WZW Theory at Higher Genera
A method to obtain explicit and complete topological solution of SU(2) Chern-Simons theory on $S^3$ is developed. To this effect the necessary aspects of the theory of coloured-oriented braids and duality properties of conformal blocks for…
We formulate a 4-dimensional higher gauge theoretic Chern-Simons theory. Its symmetry is encoded in a semistrict Lie 2-algebra equipped with an invariant non singular bilinear form. We analyze the gauge invariance of the theory and show…
We study several different $Z_2$ topological ordered states in frustrated spin systems. The effective theories for those different Z_2 topological orders all have the same form -- a Z_2 gauge theory which can also be written as a mutual…
The highest weight modules of the chiral algebra of orthogonal WZW models at level one possess a realization in fermionic representation spaces; the Kac-Moody and Virasoro generators are represented as unbounded limits of even CAR algebras.…
We consider the geometric quantisation of Chern--Simons theory for closed genus-one surfaces and semisimple complex groups. First we introduce the natural complexified analogue of the Hitchin connection in K\"{a}hler quantisation, with…
We compute the canonical partition function of 2+1 dimensional de Sitter space using the Euclidean $SU(2)\times SU(2)$ Chern-Simons formulation of 3d gravity with a positive cosmological constant. Firstly, we point out that one can work…
We propose a new procedure to embed second class systems by introducing Wess-Zumino (WZ) fields in order to unveil hidden symmetries existent in the models. This formalism is based on the direct imposition that the new Hamiltonian must be…
Three dimensional SU(2) Chern-Simons theory has been studied as a topological field theory to provide a field theoretic description of knots and links in three dimensions. A systematic method has been developed to obtain the link-invariants…
The low-energy effective action for the N=4 super Yang-Mills on the Coulomb branch is known to include an SO(6)-invariant Wess-Zumino (WZ) term for the six scalar fields. For each maximal, non-anomalous subgroup of the SU(4) R-symmetry, we…
We study the $SU(2)_k$ Wess-Zumino-Novikov-Witten (WZNW) theory perturbed by the trace of the primary field in the adjoint representation, a theory governing the low-energy behaviour of a class of strongly correlated electronic systems.…
This paper (completed March 1992) is an extensively revised and expanded version of work which appeared July 1991 on the initial incarnation of the hepth bulletin board, and which was published in the Proceedings of the Workshop on String…
Gauged Wess-Zumino-Witten theory for compact groups is considered. It is shown that this theory has fermionic BRST-like symmetry and may be exactly solved using localization approach. As an example we calculate functional integral for the…
We study the Schur index of 4-dimensional $\mathcal{N}=2$ circular quiver theories. We show that the index can be expressed as a weighted sum over partition functions describing systems of free Fermions living on a circle. For circular…
We give explicit field theoretical representations for the observables of 2+1 dimensional Chern-Simons theory in terms of gauge invariant composites of 2D WZW fields. To test our identification we compute some basic Wilson loop correlators…
The left and right zero modes of the level k SU(n) WZNW model give rise to a pair of isomorphic (left and right) mutually commuting quantum matrix algebras. For a deformation parameter q being an even (2h-th, h = k + n) root of unity each…
We present an analysis of the canonical structure of the WZW theory with untwisted conformal boundary conditions. The phase space of the boundary theory on a strip is shown to coincide with the phase space of the Chern-Simons theory on a…
It is shown how a chiral Wess-Zumino-Witten theory with globally defined vertex operators and a one-to-one correspondence between fields and states can be constructed. The Hilbert space of this theory is the direct sum of tensor products of…
We construct a family of 1D and 2D long-range SU(2) spin models as parent Hamiltonians associated with infinite dimensional matrix product states that arise from simple current correlation functions in $SU(2)_k$ WZW models. Our results…
In recent years, significant progress has been made in the study of integrable systems from a gauge theoretic perspective. This development originated with the introduction of $4$d Chern-Simons theory with defects, which provided a…
We give an explicit construction of the quantum-group generators ---local, semi-local, and global --- in terms of the group-valued quantum fields $\tilde g$ and $\tilde g^{-1}$ in the Wess-Zumino-Novikov-Witten (WZNW) theory. The algebras…