Superconductivity for other forces

Um... no.

You are presumably talking about something analagous to the phenomenon of superconductivity with respect to different forces, so the actual answer would depend a lot on what you think the word means. i.e. what would you consider "conductivity" for an EM force ... and then what would you consider to be analogous to that for something like gravity?

 

It is believed that for very high densities and low temperatures, quark matter is in a type of superconducting phase. Look up "color superconductivity" or "color-flavor locking".http://en.wikipedia.org/wiki/Color_superconductivity

I don't know the details so I can't tell you how similar it actually is to normal superconductivity.

Try googling "electroweak superconductivity" and you will find some results.

 

In a sense, our universe is already in a superconducting state with respect to the weak force, because the spontaneous symmetry breaking via Higgs mechanism (for which the Nobel prize is awarded a few days ago) makes the W and Z bosons massive. See
https://www.physicsforums.com/showpost.php?p=4306375&postcount=12

 

... oh yeah: I was using a 4-force model.
But notice how each of the above rely on some interpretation of what "superconducting" means in each context?

 

In the electroweak realm, you get dynamical electroweak superconductivity - http://arxiv.org/abs/hep-ph/0304036. From the strong force, you theoretically have color superconductivity - http://arxiv.org/abs/nucl-th/0410091. Gravity, of course, is the red headed step child. It is hypothesized such a state could produce anti gravity, but, is still considered highly speculative. I'm still unconvinced gravity is a 'force' in the same sense as the other fundamental forces.