QUANTUM STRINGS AND RANDOM SURFACES
187
The finiteness of the integral (9.160) also allows one to use the following
trick to compute it:
Q ) r d^k /c + (/c+ + q^)
3i r d^k
/ I
1
M9
W -
2q{k-q)^k^
(Inf
d^k
d^k
kl - k+q,
I s L i,
16tc ^_ J
4Snq_
Obviously this also implies:
n_
^ qi
487T q +
Let us now consider the remaining component
d^k
= 1
d^k — A
(9.164)
(9.165)
where >1 is a quadratically divergent constant which we shall fix in a
moment. So the general form of the induced action is the following:
Si,= -
f d^q (I q\
4 ^
1 q^+ ^ — k+ M)h+ +(-q) + Aq^h+ +(q)h_ ,(-q)
^ q +
+ Bq^h^_(q)h^.(-q)^Clh^.qlh^^-^qlh^_h._:\
(9.166)
where we have added another possible local counter-terms with some
constants A, B and C. The constants A, B and C can be determined from