3 research outputs found
On the Semi-Relative Condition for Closed (TOPOLOGICAL) Strings
We provide a simple lagrangian interpretation of the meaning of the
semi-relative condition in closed string theory. Namely, we show how the
semi-relative condition is equivalent to the requirement that physical
operators be cohomology classes of the BRS operators acting on the space of
local fields {\it covariant} under world-sheet reparametrizations. States
trivial in the absolute BRS cohomology but not in the semi-relative one are
explicitly seen to correspond to BRS variations of operators which are not
globally defined world-sheet tensors. We derive the covariant expressions for
the observables of topological gravity. We use them to prove a formula that
equates the expectation value of the gravitational descendant of ghost number 4
to the integral over the moduli space of the Weil-Peterson K\"ahler form.Comment: 10 pages, harvmac, CERN-TH-7084/93, GEF-TH-21/199
Gribov horizon, contact terms and \v{C}ech- De Rham cohomology in 2D topological gravity
We point out that averages of equivariant observables of 2D topological
gravity are not globally defined forms on moduli space, when one uses the
functional measure corresponding to the formulation of the theory as a 2D
superconformal model. This is shown to be a consequence of the existence of the
Gribov horizon {\it and} of the dependence of the observables on derivatives of
the super-ghost field. By requiring the absence of global BRS anomalies, it is
nevertheless possible to associate global forms to correlators of observables
by resorting to the \v{C}ech-De Rham notion of form cohomology. To this end, we
derive and solve the ``descent'' of local Ward identities which characterize
the functional measure. We obtain in this way an explicit expression for the
\v{C}ech-De Rham cocycles corresponding to arbitrary correlators of
observables. This provides the way to compute and understand contact terms in
string theory from first principles.Comment: Uses harvmac, 33 pages (big) or 20 pages (little