r - r
r - / ‘ ( r , D
The fields are transformed as:
QUANTUM STRINGS AND RANDOM SURFACES
tran sform atio n s:
237
(9.378)
(9.379)
The new action (or better to say the “minus” part of it) changes to
- J d r d f
a r
KC,f-)
a / a / - y
a r la^
• a ( r , / - ( r , D )
drdf-b(rf-)^a(r,f-)
d V d r ( b c ) j y i o i ( y ,
h '
Now let us take
/ - - r + £ .( r r )
with infinitesimal £+. We get:
(9.380)
(9.381)
S — S= ({b d^a)—jd_(ba))d + e +
From here we can read off* the energy-momentum tensor which couples
to
+ :
T__ = (bd_a) -jd_(ba) = (I -j)bd^a + jad_b
(9.382)