Let $(\tau,\sigma)$ be our coordinate system on a local path of worldsheet. For open string $\sigma \in [0,\pi]$ and the end points are different. Now if we do compactification on this string in $26$th dimension i.e. $X^{25}(\tau,\sigma)\sim X^{25}(\tau,\sigma)+R$. My doubt is depending on the length of compactification it can happen the string end points meet the end in $X^{25}$ direction like in the following drawn diagram: enter image description here This seems to imply the open string has become sort of close string in some direction. I don't understand what's going on since in Polchinski vol 1 (string theory) no diagram is drawn to clarify compactification for open string instead Wilsonian line is discussed in the compactification section of open string $(8.6)$

  • 1
    $\begingroup$ The end points of open strings can always join together to give closed strings, i.e. you can't have open strings without closed strings. What you are showing here is that an open string can join to form a closed string with a winding modes. $\endgroup$
    – Prahar
    Feb 10, 2022 at 15:46
  • $\begingroup$ @Prahar Thanks! I got the idea of winding mode for open string $\endgroup$
    – aitfel
    Feb 10, 2022 at 15:55
  • $\begingroup$ open strings cannot have winding modes of course. $\endgroup$
    – Prahar
    Feb 10, 2022 at 15:58
  • $\begingroup$ @Prahar yeah if the open string ends don't join to form a closed string then the endpoints will be different so it can unwound (because of $X^1...X^24$) $\endgroup$
    – aitfel
    Feb 10, 2022 at 16:08


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Browse other questions tagged or ask your own question.