14 research outputs found
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