Zwiebach Exercise 9.3b

[ehrenfest]

1. The problem statement, all variables and given/known data
Apparently the answer is sqrt(2 alpha') *4a. But doesn't equation 9.10 imply that the 4a should just be a 1?


2. Relevant equations



3. The attempt at a solution

[Jimmy Snyder]

It's kind of a coincidence that when I did that problem two years ago, that's what I wrote in the margin of my book. However it is not true. l_s is just a unit of length like the Planck length. It is not necessarily the length of any string. It is useful as a unit of length when doing string theory as this problem shows. The answer is 4\sqrt{2}a in units of the string length.

[ehrenfest]

I see--we need to integrate differential lengths from sigma = 0 to sigma = 2 pi. Thanks.

[Jimmy Snyder]

I see--we need to integrate differential lengths from sigma = 0 to sigma = 2 pi. Thanks.
That's for closed strings. As this is an open string, the range is different.