# Tachyon vertex operator (Polchinski's book)

• I would like to know how does Polchinski in his book "derive" what is the "tachyon vertex operator" (..as say stated in equation 3.6.25, 6.2.11..) I can't locate a "derivation" of the fact that $:e^{ikX}:$ is the tachyon vertex operator.

(..I understand that it follows from some application of the state-operator map but I can't put it together..)

• And then what is the meaning of the higher vertex operators" - which are of the form of arbitrary number of either operators of the above kind or the derivatives of $X$ w.r.t either $z$ or $\bar{z}$. (..like in equation 6.2.18..)

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I wonder if someone could make the question (v1) and answers more self-contained, preferably so one doesn't have to open Polchinski's book? – Qmechanic♦ Dec 6 '12 at 10:30
Yes please @user6818, put the equations in, I dont have a Polchinski book ... :-/ – Dilaton Apr 2 at 17:28

## 1 Answer

Polchinski explains the state-operator correspondence in section 2.8, in particular equations 2.8.3, 2.8.4, and 2.8.9.

What you call "higher vertex operators" create multiple particles (if there are multiple exponential vertex operators) with higher spin (if there are extra derivatives multiplying the exponentials).

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That was kind of my question :) Equation 2.8.3 and 2.8.4 are just definitions and I guess that the LHS of 2.8.9 is the same state as defined in open strings through 1.3.27. Now from that how does the equality of 2.8.9 follow? What is the derivation of that and why is it tachyonic? (..I presume that the tachyonic nature follows if the notation of $|0;k>$ follows the same state as described as the lightest bosonic open strings as in equation 1.3.38..) Though there does seem to be a need to derive 2.8.9 - but unlike these 3.6.1 and 3.6.25 are talking of "closed" strings.. – user6818 Dec 7 '12 at 23:39

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@user6818: Ugh. We need to start latexing equations into the posts, to make them self-contained. It's painful to have a discussion while referring to a book that I keep in a different window. Can you go back through the post and latex the equations in? – user1504 Dec 9 '12 at 14:13
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