Related papers: Chiral ring in the 4D W_3 string
Remarks are given to the structure of physical states in 2D gravity coupled to $C\leq 1$ matter. The operator algebra of the discrete state operators is calculated for the theory with non-vanishing cosmological constant.
The full cohomology ring of the Lian-Zuckerman type operators (states) in ${\hat c_M}<1$ Neveu-Schwarz-Ramond (NSR) string theory is argued to be generated by three elements $x$, $y$ and $w$ in analogy with the corresponding results in the…
This is the first in a series of papers, where we introduce and study topological spaces that realize the algebras of quasi-invariants of finite reflection groups. Our result can be viewed as a generalization of a well-known theorem of A.…
Consider a physical system for which a mathematically rigorous geometric quantization procedure exists. Now subject the system to a finite set of irreducible first class (bosonic) constraints. It is shown that there is a mathematically…
All solvable two-dimensional quantum gravity models have non-trivial BRST cohomology with vanishing ghost number. These states form a ring and all the other states in the theory fall into modules of this ring. The relations in the ring and…
We present results for the BRST cohomology of $\cW[\bfg]$ minimal models coupled to $\cW[\bfg]$ gravity, as well as scalar fields coupled to $\cW[\bfg]$ gravity. In the latter case we explore an intricate relation to the (twisted) $\bfg$…
We study a Lie algebra of formal vector fields $W_n$ with its application to the perturbative deformed holomorphic symplectic structure in the A-model, and a Calabi-Yau manifold with boundaries in the B-model. A relevant concept in the…
In a series of papers Grassi, Policastro, Porrati and van Nieuwenhuizen have introduced a new method to covariantly quantize the GS-superstring by constructing a resolution of the pure spinor constraint of Berkovits' approach. Their latest…
Recent results about topological coset models are summarized. The action of a topological ${G\over H}$ coset model ($rank\ H = rank\ G$) is written down as a sum of ``decoupled" matter, gauge and ghost sectors. The physical states are in…
In this paper, we study the perturbative aspects of the half-twisted variant of Witten's topological A-model on a complex orbifold X/G, where G is an isometry group of X. The objective is to furnish a purely physical interpretation of the…
The chiral algebra of tetrahedral molecules, derived from Fischer projections, is discussed in the framework of quantum mechanics. A quantum chiral algebra is obtained whose operators, acting as rotations or inversions, commute with the…
Progress along the line of a previous article are reported. One main point is to include chiral operators with fractional quantum group spins (fourth or sixth of integers) which are needed to achieve modular invariance. We extend the study…
We generalise the analysis carried out in [arXiv:0710.5796], and find that our previous results can be extended beyond the case of SL(N,C). In particular, we show that an equivalence--at the level of the holomorphic chiral algebra--between…
String theory on ${\rm AdS}_3\times {\rm S}^3 \times\mathbb{T}^4$ with one unit ($k=1$) of NS-NS flux is considered in the hybrid formalism of Berkovits, Vafa & Witten (BVW). Using the free field realisation of the world-sheet theory at…
Given a group G, we construct, in a canonical way, an inverse semigroup S(G) associated to G. The actions of S(G) are shown to be in one-to-one correspondence with the partial actions of G, both in the case of actions on a set, and that of…
We study the BRST-cohomology in the quantum hamiltonian reduction of affine Lie algebras of non-simply laced type. We obtain the free field realization of the $W{\bf g}$-algebra for $\bg=B_{2}$, $B_{3}$, $C_{3}$ and $G_{2}$. The $WC_{3}$…
The quantization of a free boson whose momentum satisfies a cubic constraint leads to a $c=\ha$ conformal field theory with a BRST symmetry. The theory also has a $W_\infty $ symmetry in which all the generators except the stress-tensor are…
Twisted holography relates the two-dimensional chiral algebra subsector of $\mathcal{N}=4$ SYM to the B-model topological string theory on the deformed conifold $SL(2,\mathbb{C})$. We review the relevant aspects of the duality and its two…
Six-dimensional conformal field theories with $(2,0)$ supersymmetry are shown to possess a protected sector of operators and observables that are isomorphic to a two-dimensional chiral algebra. We argue that the chiral algebra associated to…
We present the complete set of $N=1$, $D=4$ quantum algebras associated to massive superparticles. We obtain the explicit solution of these algebras realized in terms of unconstrained operators acting on the Hilbert space of superfields.…