I have a question about deriving the coupling term of string and the gauge field on brane. According to David Tong's lecture note p184/(191 in acrobat), the coupling is given by
Send−point=∫∂MdτAa(X)dXadτ
It is said that the coupling is obtained by exponentiating the vertex operator, "as described at the beginning of Section 7",
Vphoton∼∫∂Mdτζa∂τXaeip⋅x
My question is about the logic of exponentiating the vertex operator.
In the beginning of section 7 of the lecture note, in order to obtain the coupling between string and the gauge fields, the Polyakov action is extended in curved space
S=14πα′∫d2σ√ggαβ∂αXμ∂βXνGμν(X)
The coupling comes from the bending of spacetime, e.g.
Gμν(X)=δμν+hμν(X)
Z=∫DXDge−SPoly−V=∫DXDge−SPoly(1−V+12V2+…)
V=14πα′∫d2σ√ggαβ∂αXμ∂βXνhμν(X)
In order to obtain Eq. (1) from (2), where is the bending of metric?
This post imported from StackExchange Physics at 2014-03-07 16:48 (UCT), posted by SE-user user26143