Problem 14.2.2

A First Course in String Theory
 
 
14.2 Generating function for the unoriented bosonic open string theory.

~~~

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
 
 
 
2015.09.23 Wednesday (c) All rights reserved by ACHK