# Problem 14.2.2

A First Course in String Theory

14.2 Generating function for the unoriented bosonic open string theory.

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How to add “a term that implements the projection to unoriented states”?

What is the projector? $\Omega$?

$f_{os} (x)$

$= \frac{1}{x} \prod_{n=1}^\infty \frac{1}{(1-x^n)^{24}}$

$= \frac{1}{x} \left( 1 + 24 x + 324 x^2 + 3200 x^3 + ... \right)$

To keep only the odd-power terms, we should construct an odd function:

$f_{uos} (x)$

$= \frac{1}{2} \left( f_{os} (x) - f_{os} (-x) \right)$

$= \frac{1}{x} \prod_{n=1}^\infty \frac{1}{(1-x^n)^{24}} - \left( \frac{-1}{x} \prod_{n=1}^\infty \frac{1}{(1-(-x)^n)^{24}} \right)$

— Me@2015-09-17 02:27:20 PM