Related papers: On the W-gravity spectrum and its G-structure
We study the spectra of G/G coset models by computing BRST cohomology of affine Lie algebras with coefficients in tensor product of two modules. One-to-one correspondence between the spectra of $A_1^1/A_1^1$ and that of the minimal matter…
We derive the BRST cohomology of the G/G topological model for the case of A^{(1)}_{N-1} . It is shown that at level k={p/q}-N the latter describes the (p,q) W_N minimal model coupled to $W_N$ gravity (plus some extra ``topological…
$G/G$ topological field theories based on $G_k$ WZW models are constructed and studied. These coset models are formulated as Complex BRST cohomology in $G^c_k$, the complexified level $k$ current algebra. The finite physical spectrum…
The ring structure of Lian-Zuckerman states for $(q,p)$ minimal models coupled to gravity is shown to be ${\cal R}={\cal R}_0\otimes {\bf C} [w,w^{-1}]$ where ${\cal R}_0$ is the ring of ghost number zero operators generated by two elements…
We present some explicit results on the structure of singular vectors in $c=2$ Verma modules of the $\cW_3$ algebra. Using the embedding patterns of those vectors we construct resolutions for the $c=2$ irreducible modules, and thus are able…
By using a bosonization we uncover the topological gravity structure of Labastida, Pernici and Witten in ordinary $2d$ gravity coupled to $(p,q)$ minimal models. We study the cohomology class associated with the fermionic charge of the…
We generalize some of the standard homological techniques to $\cW$-algebras, and compute the semi-infinite cohomology of the $\cW_3$ algebra on a variety of modules. These computations provide physical states in $\cW_3$ gravity coupled to…
We discuss physical spectra and correlation functions of topological minimal models coupled to topological gravity. We first study the BRST formalism of these theories and show that their BRST operator $Q=Q_s+Q_v$ can be brought to $Q_s$ by…
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 discuss various techniques for computing the semi-infinite cohomology of highest weight modules which arise in the BRST quantization of two dimensional field theories. In particular, we concentrate on two such theories -- the $G/H$ coset…
We study the equivariant cohomology of a class of multi-field topological LG models, and find that such systems carry intrinsic information about $W$-gravity. As a result, we can construct the gravitational chiral ring in terms of LG…
An analysis of the BRST cohomology of the G/G topological models is performed for the case of $A_1^{(1)}$. Invoking a special free field parametrization of the various currents, the cohomology on the corresponding Fock space is extracted.…
We study the BRST cohomology for two-dimensional supergravity coupled to $\hat c \leq 1$ superconformal matter in the conformal gauge. The super-Liouville and superconformal matters are represented by free scalar fields $\phi^L$ and…
The noncritical $D=4$ $W_3$ string is a model of $W_3$ gravity coupled to two free scalar fields. In this paper we discuss its BRST quantization in direct analogy with that of the $D=2$ (Virasoro) string. In particular, we calculate the…
We classify all the first-order vertices of gravity consistently coupled to a system of 2-form gauge fields by computing the local BRST cohomology H(s|d) in ghost number 0 and form degree n. The consistent deformations are at most linear in…
Using deformation theory based on BRST cohomology, a supergravity model is constructed which interpolates through a continuous deformation parameter between new minimal supergravity with an extra U(1) gauge multiplet and standard…
Recently, the infinitesimal moduli space of heterotic $G_2$ compactifications was described in supergravity and related to the cohomology of a target space differential. In this paper we identify the marginal deformations of the…
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…
This article is devoted to the analysis of the gauge-fixed BRST cohomology complex for a matrix model endowed with a $U(2)$-gauge symmetry. After a brief introduction on the BV construction and the gauge-fixing procedure in the setting of…
In this paper we begin the study of the (dual) Steenrod algebra of the motivic Witt cohomology spectrum $H_W\mathbb{Z}$ by determining the algebra structure of ${H_W\mathbb{Z}}_{**}H_W\mathbb{Z}$ over fields $k$ of characteristic not $2$…