# Entangled closed oriented strings / closed string chains

1. Oct 11, 2006

### bjurke@gmx.de

This morning an odd thought struck me: Is it possible to consider
closed (oriented) strings which are entangled into each other in target
space (like two rings of a chain)? Due to the topologic properties of
this construction the structure should be stable, since both strings
cannot interact with each other.

But I'm wondering how to obtain such a structure in the first place.
One must certainly add a second string field to the Polyakov action
with strong constraints to ensure the entanglement to hold. Developing
this further, entire chains of closed strings should be a possible
stable structure, if the thing works for two strings. Currently I don't
know of a definite argument which would rule out such a kind of
structure - it just seams very complicated to construct it.

I searched for a while for some papers who perhaps followed a similar
idea, but did not find anything. So I would be grateful for some
further hints on this idea, or an argument why it doesn't make sense in
the first place.

Thanks,
Benjamin Jurke

2. Oct 28, 2008

### Octodude

Hi, i got quite the same idea but not in the same way...

About your idea, i believe it could exists, because with an open string theory we can construct such a weird thing. In a closed string theory, I'm not convince it is stable, because nothing can't stop it to fuse with the other one, so to interact. However, i don't think we can separate them trivially, so it is clearly not equivalent to 2 independent separated strings. But it can disintegrate into 2 separated particles ! Now is it relevant...? An other question, with the fact that the length of the strings is at Planck scale order, is the 'inside' of the string really accessible ? I mean, probably in the end, we'll have to consider fields of string, so reaching a second quantization of string, and then, in such a field theory of strings, this sort of configuration will be ejected by the Heisenberg incertitude at small distances...

Nevertheless, as i said before, i have also a similar idea. You can construct a vacuum to vacuum 1-loop amplitude with 2 closed string. You have the 2 separated rings and the 2 entangled rings. The latter are static, because it is an amplitude. And they are inequivalent, because if we cross the rings then we have a 2-loop amplitude. Is that interesting ?
I think probably no...because it will, i believe, give after some calculation a 2-loop order amplitude (maybe between 1 and 2). Because, suppose it is not equivalent to 2 separated rings, then it is an irreducible 1st order vacuum amplitude that should be counted with the same priority than the 1-loop amplitude, That is, we have a vacuum amplitude basis. So if we have an infinity of rings entangled in the first ring this will be also an irreducible 1st order vacuum amplitude that should be part of the basis. Then the vacuum 1st order amplitude is infinite, and so it is not cool. And as i think string theory is cool, it should not be at 1-loop amplitude order. Seriously, as it is not equivalent to 2 1-loop amplitude, i think it will be next order, so not so important.

So, i don't say we don't care, but it is not of first priority...

Hope it helps a bit...

Flavien Kiefer