Question

How to integrate over infinitesimal conformal transformation?

Answer 1

Polchinski Vol. 1 (Sec. 2.4): I'm trying to derive

(∂w)2T(w)=T(z)−c12{w,z}(2.4.26)(2.4.26)(∂w)2T(w)=T(z)−c12{w,z}

from its infinitesimal version given by

δT(w)=−ϵ(w)∂T(w)−2ϵ'(w)T(w)−c12ϵ'''(w).(2.4.24)(2.4.24)δT(w)=−ϵ(w)∂T(w)−2ϵ′(w)T(w)−c12ϵ′′′(w).

How do you do that?

Can anyone, please, also tell me how does one integrate over an infinitesimal variation in general?

Answer 2

Conformal transformations in d dimensions . .... 5.9 Integration over moduli . ..... can study the action of the infinitesimal conformal transformations on a space of.