Related papers: Lectures on W algebras and W gravity
The $w_{1+\infty}$ symmetry algebra appears in the Einstein--Yang--Mills theory, proposed recently by Strominger. In this paper, we derive the supersymmetric $w_{1+\infty}$ symmetry by using the known results on the operator product…
In this paper, we study gravitational symmetry algebras that live on 2-dimensional cuts $S$ of asymptotic infinity. We define a notion of wedge algebra $\mathcal{W}(S)$ which depends on the topology of $S$. For the cylinder $S=\mathbb{C}^*$…
It was recently shown that gl^(1|1) admits an infinite family of simple current extensions. Here, these findings are reviewed and explicit free field realisations of the extended algebras are constructed. The leading contributions to the…
It has been known for some time that $W$ algebras can be realised in terms of an energy-momentum tensor together with additional free scalar fields. Some recent results have shown that more general realisations are also possible. In this…
The linearized spectrum and the algebra of global symmetries of conformal higher-spin gravity decompose into infinitely many representations of the conformal algebra. Their characters involve divergent sums over spins. We propose a suitable…
Topological conformal field theories based on superconformal current algebras are constructed. The models thus obtained are the supersymmetric version of the $G/G$ coset theories. Their topological conformal algebra is generated by…
We review some aspects of the construction of self-dual gravity and the associated field theory of ${\cal N}=2$ strings in terms of two-dimensional sigma models at large $N$. The theory is defined through a large $N$ Wess-Zumino-Witten…
Lectures given at the Trieste Summer School, 1992. These notes are an update of my review article "Classical and Quantum W-Gravity", preprint QMW-92-1, published in in "Strings and Symmetries 1991", with some extra material on W-geometry,…
We review some aspects of gauged WZW models. By choosing a nilpotent subgroup as gauge group, one is lead to three main applications: the construction of field theories with an extended conformal symmetry, the construction of the effective…
We generalize, to any space-time dimension, the unitarity bounds of highest weight UIR's of the conformal groups with Lie algebras $so(2,d)$. We classify gauge theories invariant under $so(2,d)$, both integral and half-integral spins. A…
It is shown that in the presence of a nonvanishing cosmological constant, Strominger's infinite-dimensional $\mathrm{w_{1+\infty}}$ algebra of soft graviton symmetries is modified in a simple way. The deformed algebra contains a subalgebra…
We discuss the infinite dimensional algebras appearing in integrable perturbations of conformally invariant theories, with special emphasis in the structure of the consequent non-abelian infinite dimensional algebra generalizing $W_\infty$…
In this paper, we investigate the spinor field realizations of the $W_{2,4}$ algebra, making use of the fact that the $W_{2,4}$ algebra can be linearized through the addition of a spin-1 current. And then the nilpotent BRST charges of the…
We explore the connection between super $\mathcal{W}$-algebras ($\mathcal{SW}$-algebras) and $\mathrm{G}$-structures with torsion. The former are realised as symmetry algebras of strings with $\mathcal{N}=(1,0)$ supersymmetry on the…
Symmetry transformations of the space-time fields of string theory are generated by certain similarity transformations of the stress-tensor of the associated conformal field theories. This observation is complicated by the fact that, as we…
We construct $N=2$ super-$W_{n+1}$ strings and obtain the complete physical spectrum, for arbitrary $n \ge 2$. We also derive more general realisations of the super-$W_{n+1}$ algebras in terms of $k$ commuting $N=2$ super energy-momentum…
We define a generalized form of $L_\infty$-algebras called $E_2L_\infty$-algebras. As we show, these provide the natural algebraic framework for generalized geometry and the symmetries of double field theory as well as the gauge algebras…
The fact that certain non-linear $W_{2,s}$ algebras can be linearized by the inclusion of a spin-1 current can provide a simple way to realize $W_{2,s}$ algebras from linear $W_{1,2,s}$ algebras. In this paper, we first construct the…
Casimir W-algebras are shown to exist in such a way that the conformal spins of primary(generating) fields coincide with the orders of independent Casimir operators. We show here that this coincidence can be extended further to the case…
SW(3/2,2) superconformal algebra is W algebra with two Virasoro operators. The Kac determinant is calculated and the complete list of unitary representations is determined. Two types of extensions of SW(3/2,2) algebra are discussed. A new…