Q:

Does the federation have slipstream or transwarp technology in Star Trek: Into Darkness?

I enjoyed the story of into darkness, but some of the events have been nagging at me since I first saw them on screen. I am convinced that the federation has either transwarp or slipstream technology and that the NCC-1701 and Dreadnought were equipped with them. Consider the following:

At warp factor 9.975 it is possible to travel 132 light years in one month (http://en.memory-alpha.org/wiki/Warp_factor). Qo'nos is 110 light years from earth. 
When the NCC-1701 is tasked with a strike on Qo'nos, they appear to make the journey there very rapidly. However, I can imagine someone being wishy washy over whether we just didn't see the whole trip. Let's talk about the trip back.
The NCC-1701 was pursued by the Dreadnought when it attempted to retreat to earth from a position near the klingon's home solar system. 

In this sequence, the enterprise is surprised that it is overtaken while at warp. Normal warp physics allow for this to happen, so it seems possible that the Enterprise is employing a technology which requires special mastery in order to travel at different velocities. Humans were doing this (with warp) shortly after zhefram cochrane flew his first warp ship, so I think this suggests they are using a new technology.
The enterprise appears to be using a conduit when it travels. Normal warp physics involve creating a bubble around the ship which propels it. The imagery of a conduit is never shown except when involving a slipstream or transwarp conduit. 
When the Enterprise is knocked out of warp by the Vengeance, it appears to exit a conduit. They are thrown violently back into normal space, even losing attitude control for a period of time. This was never observed to happen when a ship is knocked out of warp, but it was observed to happen when a ship fell out of a slipstream.  
The time it took the Eneterprise to flee from Qo'nos to the Sol system was very short, on the order of minutes. When the Enterprise was knocked out of warp it was already inside the Sol System. 

The only explanation I can imagine is that Spock supplied the federation with very advanced propulsion technology. However, this seems difficult for me to believe, because whenever time travel is involved, federation command officers are forever concerned with accidentally altering the time line (for good or ill). I would think Spock would adhere to this moral principle in general, though I could forgive his hasty decision to supply his friends with transwarp beaming technology as he did just see his planet obliterated. Assuming that, my best guess is that the federation extrapolated new propulsion technology based on the transwarp beaming technology supplied by Spock. 
However, if the federation really did have this kind of propulsion technology, I have difficulty believing they would be at all concerned with a possible Klingon war(which they appear to be). They would have an absurd tactical advantage. 

A:

To answer your question, no, the ships do not have any new form of engines that we know of.  They are operating at speeds/time frames other canon has provided. Canon however conflicts with itself over and over again so there really aren't standards to go by here. Basically warp speed equals X and take Y to get there, except when getting from point A to point B actually only takes Z. 
In the pilot episode of Star Trek: Enterprise (Broken Bow, Part I and II), it took the Enterprise four days to reach Qo'Nos from Earth at warp 4.5. I would imagine that 100 years later the same trip would be remarkably faster.  
Also in the first movie it was stated that reaching Vulcan would take about an hour. Vulcan has been stated to be about 16 light years from Earth, so at that speed reaching Qo'Nos would take about 7 hours, a reasonable amount of time given scenes in the movie. However, I'm not finding any measurements for how far Qo'Nos actually is from Earth.
And from Memory-Alpha:

As a comparison, in Star Trek VI: The Undiscovered Country, the internal clock of the USS Enterprise-A read 08:27 as the ship left Earth Spacedock and 16:12 when it arrived to the edge of Klingon space to meet up with Kronos One. A trip of a little under 8 hours. 

