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

Lie-Poisson groups and the Miura transformation

We point out that the recent proof of the Kupershmidt-Wilson theorem by Cheng and Mas-Ramos is underpinned by the Lie-Poisson property of the second Gel'fand-Dickey bracket. The supersymmetric Kupershmidt-Wilson theorem is also proved along these same lines. Finally we comment on the possible repercussions in the problem of the coproduct for W-algebras.Comment: .dvi file, uses AMSFonts 2.1+, 10 pages (5 physical pages in landscape mode), no figure

Branes at angles and calibrated geometry

In a recent paper, Ohta and Townsend studied the conditions which must be satisfied for a configuration of two intersecting M5-branes at angles to be supersymmetric. In this paper we extend this result to any number of M5-branes or any number of M2-branes. This is accomplished by interpreting their results in terms of calibrated geometry, which is of independent interest.Comment: 16 pages, LaTeX2e (Minor correction in next to last paragraph of section 5.2

Planes, branes and automorphisms: I. Static branes

This is the first of a series of papers devoted to the group-theoretical analysis of the conditions which must be satisfied for a configuration of intersecting M5-branes to be supersymmetric. In this paper we treat the case of static branes. We start by associating (a maximal torus of) a different subgroup of Spin(10) with each of the equivalence classes of supersymmetric configurations of two M5-branes at angles found by Ohta & Townsend. We then consider configurations of more than two intersecting branes. Such a configuration will be supersymmetric if and only if the branes are G-related, where G is a subgroup of Spin(10) contained in the isotropy of a spinor. For each such group we determine (a lower bound for) the fraction of the supersymmetry which is preserved. We give examples of configurations consisting of an arbitrary number of non-coincident intersecting fivebranes with fractions: 1/32, 1/16, 3/32, 1/8, 5/32, 3/16 and 1/4, and we determine the resulting (calibrated) geometry.Comment: 26 pages (Added a reference and modified one table slightly.

More D-branes in the Nappi-Witten background

We re-examine the problem of determining the possible D-branes in the Nappi-Witten background. In addition to the known branes, we find that there are also D-instantons, flat euclidean D-strings and curved D-membranes admitting parallel spinors, all of which can be interpreted as (twisted) conjugacy classes in the Nappi-Witten group.Comment: 21 pages, 4 figures. (A small correction in Section 2.4