• Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.


PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback


(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,047 questions , 2,200 unanswered
5,345 answers , 22,709 comments
1,470 users with positive rep
816 active unimported users
More ...

  Question on the Hagedorn tower in Type I string theory

+ 3 like - 0 dislike

In a previous question (Mass spectrum of Type I string theory), I had asked about the mass spectrum of Type I string theory. I got a response saying that it is a Hagedorn tower. However, my source does not discuss much about Type I string theory (it only discusses Type IIA and Type IIB) so I searched for more sources. Yet, all the sources (all some lecture notes) I got, for some reason stopped at Type IIA and Type IIB string theories.

So my question is, what is really the mass spectrum defining the Hagedorn tower? Is it something analogous to the Type II Mass Spectrums? $ m= \sqrt{\frac{2\pi T}{c_0}\left(N+\tilde N -a-\tilde a\right)}$


asked May 15, 2013 in Theoretical Physics by dimension10 (1,985 points) [ revision history ]
edited Apr 25, 2014 by dimension10

2 Answers

+ 3 like - 0 dislike

Hagedorn spectrum just means that the density of states varies exponentially with the energy/mass. $m^2$ (asymptotically) given by the "level" (N) of the state (upto a sqrt). The number of states at level $N$ corresponds to the possible partitions of $N$ into different oscillator modes. That means that the number of states at level $N$ will increase exponentially (for large $N$). Taking a square-root (sicne we want how #states scales with $m$) still leaves an exponential, giving us a Hagedorn spectrum.

This post imported from StackExchange Physics at 2014-03-09 09:15 (UCT), posted by SE-user Siva
answered May 16, 2013 by Siva (720 points) [ no revision ]
+ 0 like - 0 dislike

Here is my solution.

For the Ramond Ramond Sector, $${m_\rm{I}} = \frac{{\left[ {\hat a_ + ^\mu ,\hat{\tilde a}_ + ^\nu } \right]}}{2}{m_{{\rm{IIB}}}}$$

For the Neveu-Schwarz Neveu-Schwarz Sector, $${m_\rm{I}} = \frac{{\left[ {\hat d_ {-1/2} ^\mu ,\hat{\tilde d}_{-1/2} ^\nu } \right]}}{2}{m_{{\rm{IIB}}}}$$

For the Ramond Neveu-Schwarz Sector or the Neveu-Schwarz Ramond Sector, $${m_\rm{I}} = \frac{{{{\hat a}_ + }\hat d_{ - 1/2}^\mu - {{\hat{\tilde a}}_ + }\hat{ \tilde d}_{ - 1/2}^\mu }}{2}{m_{{\rm{IIB}}}}$$

My reasoning is that the mass spectrum is linear in the state vectors.

answered May 17, 2013 by dimension10 (1,985 points) [ revision history ]
edited Aug 30, 2014 by dimension10

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights