Evolution of fixed-end strings and the off-shell disk amplitude Original Research Article

An exact integral expression is found for the amplitude of a bosonic string with ends separated by a fixed distance R evolving over a time T between arbitrary initial and final configurations. It is impossible to make a covariant subtraction of a divergent quantity which would render the amplitude nonzero. It is suggested that this fact (and not the tachyon) is responsible for the lack of a continuum limit of regularized random-surface models with target-space dimension greater than one. It appears consistent, however, to remove this quantity by hand. The static potential of Alvarez and Arvis V(R), is recovered from the resulting finite amplitude for R>Rc=π((d−2)α′)/3. For R