Along the lines of Kelvin's idea, discussed in the comments, Buniy and Kephart wrote a speculative paper in 2002 that the mass spectrum of glueballs in QCD might be related to the spectrum of lengths of tightened knots. Here's a figure from their paper, comparing some experimental masses to lengths of some knots:
The model in their paper argues that the mass of a glueball (viewed as some kind of flux tube) should be proportional to the length of the tube, and hence the knot energy considered here is the ropelength of knots.
I'm not an expert on QCD so take all of the following with a grain of salt.
Before you get too excited, this model so far as I can tell is based on some phenomenological considerations, not QCD itself, and furthermore, their identifications of glueball states with knots is just the best fit of some experimental masses to corresponding entries in a table of knot lengths. As the final section of their paper says, there are some knots without measured glueball states, more importantly, it's my impression that QCD is not understood well enough to confirm that these measured masses are indeed all glueballs, e.g. the state at 1270 MeV also has a quark model interpretation.
