Why heterotic strings avoid the tachyon problem of bosonic strings

[Demystifier]

The problem with bosonic strings is the fact that they contain a tachyon.
Why that is not a problem for the bosonic part of heterotic strings?

 

[R.X.]

The "standard" heterotic string is not a direct product of a (left-moving) bosonic string with a (right-moving) superstring, but it is a "correlated" product. That's why the bosonic string tachyon does not need to appear, and in fact it cannot appear if the theory has space-time supersymmetry (as applies for the standard SUSY 10d heterotic string).

But one can also construct heterotic strings without supersymmetry, either in ten or in less than ten dimensions. In these cases tachyons typically do appear.

 

[Demystifier]

Thanks R.X.!
Perhaps you could also answer my questions posed in
https://www.physicsforums.com/showthread.php?t=148575 ?

 

[Demystifier]

Now I am able to answer my question by myself.
The point is that the tachyon is the GROUND STATE of the string, which is a unique state. Thus, there is not a right-moving tachyon and a left-moving tachyon, but only one tachyon.
In the heterotic theory we have supersymmetry only in the right sector, so we can apply the GSO projection only in that sector, but the tachyon is a common state of BOTH sectors. Therefore, the GSO projection that removes tachyon from the right sector removes it also from the left sector as well.

Now it seems simple, but it took time until I realized that simple point. :)