I am aware that particles in string theory are different vibrating modes of strings. I am also aware that compactification leads to emergent fields from the parts of the metric of the compactified dimensions (I'm assuming this works the same way as in the Kaluza- Klein model). My question is whether particles arising from the quantization of these fields are treated differently from the string particles?

If yes then how are the usual problems of quantum field theory subverted for these fields?

If no then how the differences are reconciled?

An answer without delving too much into technicalities of string theory would be appreciated, if possible since I have no formal knowledge in string theory.

  • $\begingroup$ Classic Kaluza-Klein obtains gauge fields from the metric of the compactified dimensions. Quantum mechanically, the metric equals gravitons, which in string theory are closed strings, so any stringy implementation of classic KK should ultimately involve closed strings... $\endgroup$ Oct 27, 2018 at 10:07
  • $\begingroup$ But string theory is full of technical subtleties, as well as entirely new phenomena (like strings that wind all the way around the extra dimensions) which have a complicated interplay with older phenomena; which is why I am just making a sketchy answer in a comment, for now. $\endgroup$ Oct 27, 2018 at 10:09
  • $\begingroup$ @MitchellPorter oh cool i hope you could expand more on that in a full answer explaining how exactly these extra dimensional terms (which can be readily interpreted as vector or scalar fields in KK theory) can be interpreted as string worldsheets and also talk about the winding effects, subject of course to the hope that it can be explained with just basic concepts $\endgroup$
    – alex
    Oct 27, 2018 at 11:34

1 Answer 1


My question is whether particles arising from the quantization of these fields are treated differently from the string particles?

There is no such distinction - all states are stringy states. You start with your solutions for closed (gravity) and open (gauge) strings in flat space, and you compactify on an $S^1$ for example, and ask what is the spectrum now. You do this by compactifying this one spatial direction in the solutions for worldsheet.

The first type of new excitations, Kaluza-Klein states, are completely analogues to what you find in field theory due to the quantisation of momentum in the compact direction. But these are still string states.

The new stringy effect comes from allowing more general boundary conditions for the fields on the world-sheet. For the closed string we would impose $X(\sigma +2\pi)=X(\sigma)$, but now we may relax this in the $S^1$ direction $X^{c}$: \begin{equation} X^{c}(\sigma +2\pi)=X^{c}(\sigma) +2\pi \omega R \end{equation} where $\omega$ is the winding number, telling you how many times the string is winding around the $S^1$.

To go into more technical details would require to talk about mode solutions for the worldsheet and the quantised states.

  • $\begingroup$ can you write compactification of metric, Kalb-Ramond field, differential forms etc Just by boundary condition on the worldsheet? Just by putting boundary condition on worldsheet fields, can you write compactified theory? $\endgroup$
    – Hkw
    Nov 9, 2018 at 20:15

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