I L NUOVO C I M E N T O VOL. 79 A, lq. 1 1 Gennaio 1984
Stochastic Geometry of the 0~ Fermionic Strings.
S. C~.COTTI
Scuola Norma~e Superiore - Pisa (Nuovo Cimento A, 76, 627 (1983))
PACS. 11.90. - Other topics in general field and p a r t i c l e theory.
A f t e r the p u b l i c a t i o n of t h e p a p e r , I l e a r n t t h a t a ~reatment of t h i s string model similar to the one in sect. 2 was p r e v i o u s l y given b y F~,~DKIN and TS~YLIN (~,2). These authors found t h a t t h e sign of the k i n e t i c t e r m for t h e U~ a n o m a l y field (that is t h e B-field in our notation) is opposite to t h a t of t h e conformal f a c t o r (the A-field). This result was confirmed b y t h e a u t h o r s of ref. (3). Hence eq. (2.14) m u s t be s u b s t i t u t e d b y
(1) W =
of[
8z ( ~ ' u A ) 2 - (O~B)e § v~g,p + p2 exp [2:r -~The same change is needed in eq. (2.21).
The other sections need no change, b u t t h e y a p p l y to t h e h r = 2 super-Liouville model
(2)
~e = ~ , ~ + ~ [ e x p [~]]~ + ~ exp [ ~ ] ~ I - V - } ~ + b.c. ,
/1 + n~
]
which, because of the difference in sign between eqs. (1), (2), does not correspond directly to the string model, as was erroneously s t a t e d in the p a p e r . Of course, from the p o i n t of view of stochastic s u p e r s y m m e t r y , the I = 2 super-Liouville model r e m a i n s a v e r y i n t e r e s t i n g system (for instance, i t has A = cr as we can see b y solving t h e SehrSdinger equation for its one-dimensional c o u n t e r p a r t ) , even if is not related, in a direct way, to string t h e o r y .
* * *
I t h a n k t h e a u t h o r s of ref. (1,3) for t h e i r r e m a r k s on t h e p r e s e n t paper.
(1) ]~. S. FRADKIN a n d A. A. TSEYLIN: Phys. Lell. B, 106, 63 (1981). (2) E. S. FRADKIN a n d A. A. TSEYLIN-' A n n . Phys. (N. Y.), 413 (1982).
(*) P. DI VECOmA, B. DURHUUS, P. 0LESEN a n d J. L. PETERSEN: .Nllc1. Phys. B, 217, 195 (1982).
