A First Course in String Theory
14.2 Generating function for the unoriented bosonic open string theory.
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What is the difference between oriented and unoriented bosonic open strings?
p.268: “The theory of unoriented strings is obtained by restricting the oriented string spectrum to the set of states that are invariant under the action of . Unoriented strings are not strings without orientation: they should be viewed as a quantum superposition of states that as a whole, are invariant under orientation reversal.”
An unoriented state is a superposition of 2 opposite oriented states.
— Me@2015.07.03 12:12 PM
Clue 2: “… adding a term that implements the projection to unoriented states.”
Equation (14.63):
The generating function for bosonic open string theory is
Clue 3: p.278 Problem 12.12e
An unoriented string state is a superposition of two opposite-oriented string states. An unoriented string state has twist invariant.
We can choose to keep all states with
.
We can also choose the states with . However, they are only valid for the basis states, not for other states, because other states are superpositions of basis states. The relative phase between basis states are physical in a superposition.
Effectively, the states with
are the only possible choices. In other words,
must be even.
— This answer is my guess. —
For the unoriented open strings, we should keep only the even powers of :
— This answer is my guess. —
— Me@2015-09-17 02:27:20 PM
2015.09.21 Monday (c) All rights reserved by ACHK