Entangled closed oriented strings / closed string chains
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.