Zwiebach Exercise 9.3b: Solving for 4a in Equation 9.10

[ehrenfest]

Homework Statement

Apparently the answer is sqrt(2 alpha') *4a. But doesn't equation 9.10 imply that the 4a should just be a 1?

Homework Equations

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.