Evolution of Fixed-End Strings and the Off-Shell Disk Amplitude

الأصل · EN

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 covariant quantity which would render the amplitude non-zero. 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. For R<Rc, we find V(R)=-∞, instead of the usual tachyonic result. A rotation-invariant expression is proposed for special cases of the off-shell disk amplitude. None of the finite amplitudes discussed are Nambu or Polyakov functional integrals, except through an unphysical analytic continuation. We argue that the Liouville field does not decouple in off-shell amplitudes, even when the space-time dimension is twenty-six.