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In Polchinski's string theory vol 1, p. 23, it is said "It is a complicated question whether the bosonic string has any stable vacuum, and the answer is not known."

The book was published on 1998. What is the current answer of this question? Is bosonic string a realistic theory nowadays?

In addition, the ground state here is $$|0;k \rangle $$, not $$| \mathrm{vacuum} \rangle$$. Is that because the latter one is absolute nothing so we don't study?

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Thanks a lot. Would you provide a reference about no tachions in 26 dimensional bosonic string theory? Polchinski's book seems say there is tachyon :( – user26143 Jul 14 '13 at 16:48
@Dilaton The 26D 'vacuum' has tachyonic excitations. It isn't stable. – user1504 Jul 14 '13 at 16:57
The answer is still not known. – user1504 Jul 14 '13 at 16:59
@BebopButUnsteady: Bosonic ST isn't research levelp, shalll I remove the tag? – centralcharge Aug 2 '13 at 12:59

The tachyon mode in the open string spectrum is an indication that as a perturbation theory it describes the perturbation about an unstable vacuum. In 1999 Ashoke Sen realized that -- since the open string propagates with its endpoints on the space-filling D25-brane -- that instability must be the instability of the D25, which wants to decay to a "true bosonic string vacuum", usually called now the tachyon vacuum.

This conjecture became famous as "Sen's conjecture". It was subsequently checked to be true by numerical means in open bosonic string field theory. Moreover, using string field theory it became possible to study that non-perturbative state in which the D25-brane is indeed gone. There were several arguments that indeed in the vicinity of this state the perturbative open string has disappeared and turned into the closed bosonic string.

A breakthrough happened in 2005, when Martin Schnabl found an analytic expression for this "tachyon vacuum" in arXiv:hep-th/0511286.

For more references see here.

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This doesn't answer the question. It explains the fate of the open string tachyons. But it doesn't get rid of the closed string tachyons. It is not known what, if anything, they condense to. That's why I said "The answer is still not known.". – user1504 Jul 14 '13 at 21:10
I wouldn't say so. Also the closed string tachyon condensation has been studied with avail, and better understood, if admittedly less so than the open string tachyon. A list of references is here . – Urs Schreiber Jul 15 '13 at 9:26
I'm aware of those papers. And I stand by my point: The critical question is whether the closed string tachyon condensation can be understood. Classical solutions to the perturbative string theory are interesting, but they aren't enough to say that we know what the answer is. (And I'll leave off here, before this turns into an argument about what the word 'known' makes known.) – user1504 Jul 15 '13 at 12:54

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