4 research outputs found
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
On a coordinate independent description of string worldsheet theory
We study worldsheet conformal invariance for bosonic string propagating in a
curved background using the hamiltonian formalism. In order to formulate the
problem in a background independent manner we first rewrite the worldsheet
theory in a language where it describes a single particle moving in an
infinite-dimensional curved spacetime. This language is developed at a formal
level without regularizing the infinite-dimensional traces. Then we adopt
DeWitt's (Phys.Rev.85:653-661,1952) coordinate independent formulation of
quantum mechanics in the present context. Given the expressions for the
classical Virasoro generators, this procedure enables us to define the
coordinate invariant quantum analogues which we call DeWitt-Virasoro
generators. This framework also enables us to calculate the invariant matrix
elements of an arbitrary operator constructed out of the DeWitt-Virasoro
generators between two arbitrary scalar states. Using these tools we further
calculate the DeWitt-Virasoro algebra in spin-zero representation. The result
is given by the Witt algebra with additional anomalous terms that vanish for
Ricci-flat backgrounds. Further analysis need to be performed in order to
precisely relate this with the beta function computation of Friedan and others.
Finally, we explain how this analysis improves the understanding of showing
conformal invariance for certain pp-wave that has been recently discussed using
hamiltonian framework.Comment: 32 pages, some reorganization for more elaborate explanation, no
change in conclusio