26 research outputs found
Topological Field Theory and Rational Curves
We analyze the superstring propagating on a Calabi-Yau threefold. This theory
naturally leads to the consideration of Witten's topological non-linear
sigma-model and the structure of rational curves on the Calabi-Yau manifold. We
study in detail the case of the world-sheet of the string being mapped to a
multiple cover of an isolated rational curve and we show that a natural
compactification of the moduli space of such a multiple cover leads to a
formula in agreement with a conjecture by Candelas, de la Ossa, Green and
Parkes.Comment: 20 page
Target Space Duality between Simple Compact Lie Groups and Lie Algebras under the Hamiltonian Formalism: I. Remnants of Duality at the Classical Level
It has been suggested that a possible classical remnant of the phenomenon of
target-space duality (T-duality) would be the equivalence of the classical
string Hamiltonian systems. Given a simple compact Lie group with a
bi-invariant metric and a generating function suggested in the physics
literature, we follow the above line of thought and work out the canonical
transformation generated by together with an \Ad-invariant
metric and a B-field on the associated Lie algebra of so that
and form a string target-space dual pair at the classical level under
the Hamiltonian formalism. In this article, some general features of this
Hamiltonian setting are discussed. We study properties of the canonical
transformation including a careful analysis of its domain and image. The
geometry of the T-dual structure on is lightly touched.Comment: Two references and related comments added, also some typos corrected.
LaTeX and epsf.tex, 36 pages, 4 EPS figures included in a uuencoded fil
Mirror Manifolds in Higher Dimension
We describe mirror manifolds in dimensions different from the familiar case
of complex threefolds. We emphasize the simplifying features of dimension three
and supply more robust methods that do not rely on such special characteristics
and hence naturally generalize to other dimensions. The moduli spaces for
Calabi--Yau -folds are somewhat different from the ``special K\"ahler
manifolds'' which had occurred for , and we indicate the new geometrical
structures which arise. We formulate and apply procedures which allow for the
construction of mirror maps and the calculation of order-by-order instanton
corrections to Yukawa couplings. Mathematically, these corrections are expected
to correspond to calculating Chern classes of various parameter spaces (Hilbert
schemes) for rational curves on Calabi--Yau manifolds. Our results agree with
those obtained by more traditional mathematical methods in the limited number
of cases for which the latter analysis can be carried out. Finally, we make
explicit some striking relations between instanton corrections for various
Yukawa couplings, derived from the associativity of the operator product
algebra.Comment: 44 pages plus 3 tables using harvma
Simplifying superstring and D-brane actions in AdS(4) x CP(3) superbackground
By making an appropriate choice for gauge fixing kappa-symmetry we obtain a
relatively simple form of the actions for a D=11 superparticle in AdS(4) x
S(7)/Z_k, and for a D0-brane, fundamental string and D2-branes in the AdS(4) x
CP(3) superbackground. They can be used to study various problems of string
theory and the AdS4/CFT3 correspondence, especially in regions of the theory
which are not reachable by the OSp(6|4)/U(3) x SO(1,3) supercoset sigma-model.
In particular, we present a simple form of the gauge-fixed superstring action
in AdS(4) x CP(3) and briefly discuss issues of its T-dualization.Comment: 1+36 pages, v2,v3 clarifications and references adde
Gauging and symplectic blowing up in nonlinear sigma-models: I. point singularities
In this paper a two dimensional non-linear sigma model with a general
symplectic manifold with isometry as target space is used to study symplectic
blowing up of a point singularity on the zero level set of the moment map
associated with a quasi-free Hamiltonian action. We discuss in general the
relation between symplectic reduction and gauging of the symplectic isometries
of the sigma model action. In the case of singular reduction, gauging has the
same effect as blowing up the singular point by a small amount. Using the
exponential mapping of the underlying metric, we are able to construct
symplectic diffeomorphisms needed to glue the blow-up to the global reduced
space which is regular, thus providing a transition from one symplectic sigma
model to another one free of singularities.Comment: 32 pages, LaTex, THEP 93/24 (corrected and expanded(about 5 pages)
version