Q2. What is the function of the bosonized theory?
The correlation functions containing spin fields are also of the form (19), with q= + ½, since the spin fields are given by the vertex operators exp( + i½+0) in the bosonized theory.
Q3. What is the function of the reparametrization ghosts?
The reparametrization ghosts b and c correspond to the case 2 = 2, a = 0; the ~,~ correlation functions follow from (18) with 2--½.
Q4. what is the prescription for a commuting system?
There it is shown that the commuting (fl, y) ghost system can be replaced by a scalar field ~0 coupled to a background charge Q= - 2 and two conjugate anti-commuting fields ~ and q with conformal spin 0 respectively 1. The prescription readsfl(z) = 0 ~ ( z ) exp[-~0(z)] , y ( z ) = q ( z ) exp[~(z)] .
Q5. What is the BRST-invariance of the amplitudes?
as the authors will show below, for on-shell amplitudes it follows from BRST-invariance that the residues of the unphysical poles in j,; (z) are given by total derivatives on Mg, so that supersymmetry is restored after the integration over the moduli mi.
Q6. What is the quotient of two r's?
For us it is sufficient to know the quotient of two ~r's:a(z) O(z-Ep,+A) E(w, pi) (22) a(w) - O(w-Yp,+J) [I E(z,p,)is independent of the Pi and furthermore that a(z) has no zeroes or poles [7,12].
Q7. What is the proof for the amplitude of the vacuum?
So the authors conclude that the vacuum ampli tude (2) , being the integral of a total derivative on Mg, indeed vanishes to all orders ~1.Conclusion.