I am reading Polchinski's review on AdS/CFT https://arxiv.org/abs/1010.6134.
I have a very simple question, and please help me out. Thanks in advanced.
The question abou formula (3.19)
The scalarbulk effective action is given by
S0,cl=−12LD−1∫dzdDxϕcl(◻−m2)ϕcl+η2ϵ1−D∫dDxϕcl∂ϵϕcl
The bdy action is
Sb=ηΔ−2ϵ−D∫dDxϕ2(ϵ,x)
The variation of the whole action is given by
δ(S0,cl+Sb)=ηϵ−D∫dDxδϕcl(ϵ∂ϵ−Δ−)ϕcl
My question is why there is no such term ∫dDxϕclϵ∂ϵδϕcl in the variation of the action?