N=2 structures in all string theories

The BRST cohomology of any topological conformal field theory admits the structure of a Batalin--Vilkovisky algebra, and string theories are no exception. Let us say that two topological conformal field theories are ``cohomologically equivalent'' if their BRST cohomologies are isomorphic as Batalin--Vilkovisky algebras. What we show in this paper is that any string theory (regardless of the matter background) is cohomologically equivalent to some twisted N=2 superconformal field theory. We discuss three string theories in detail: the bosonic string, the NSR string and the W_3 string. In each case the way the cohomological equivalence is constructed can be understood as coupling the topological conformal field theory to topological gravity. These results lend further supporting evidence to the conjecture that _any_ topological conformal field theory is cohomologically equivalent to some topologically twisted N=2 superconformal field theory. We end the paper with some comments on different notions of equivalence for topological conformal field theories and this leads to an improved conjecture.Comment: 23 pages (12 physical pages), .dvi.uu (+ some hyperlinks

Deformations of M-theory Killing superalgebras

We classify the Lie superalgebra deformations of the Killing superalgebras of some M-theory backgrounds. We show that the Killing superalgebras of the Minkowski, Freund--Rubin and M5-brane backgrounds are rigid, whereas the ones for the M-wave, the Kaluza--Klein monopole and the M2-brane admit deformations, which we give explicitly.Comment: 20 pages (v3: a number of signs and a couple of factors have changed without affecting the result. v4: yet more sign changes, but results remain unchanged. v5: this is becoming absurd... but the signs ought to be correct now! v6: no more sign changes, but section 5.2 on the MKK monopole has been partially rewritten and some relevant references have been added.

Metric Lie n-algebras and double extensions

We prove a structure theorem for Lie n-algebras possessing an invariant inner product. We define the notion of a double extension of a metric Lie n-algebra by another Lie n-algebra and prove that all metric Lie n-algebras are obtained from the simple and one-dimensional ones by iterating the operations of orthogonal direct sum and double extension.Comment: 10 page

A new maximally supersymmetric background of IIB superstring theory

We present a maximally supersymmetric IIB string background. The geometry is that of a conformally flat lorentzian symmetric space G/K with solvable G, with a homogeneous five-form flux. We give the explicit supergravity solution, compute the isometries, the 32 Killing spinors, and the symmetry superalgebra, and then discuss T-duality and the relation to M-theory.Comment: 17 page

The Classical Limit of W-Algebras

We define and compute explicitly the classical limit of the realizations of $W_n$ appearing as hamiltonian structures of generalized KdV hierarchies. The classical limit is obtained by taking the commutative limit of the ring of pseudodifferential operators. These algebras---denoted $w_n$---have free field realizations in which the generators are given by the elementary symmetric polynomials in the free fields. We compute the algebras explicitly and we show that they are all reductions of a new algebra $w_{\rm KP}$, which is proposed as the universal classical $W$-algebra for the $w_n$ series. As a deformation of this algebra we also obtain $w_{1+\infty}$, the classical limit of $W_{1+\infty}$.Comment: (14 pages