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In many movies and in the popular culture wormholes are often referenced, as well as "faster than light travel", which seems almost to be the same thing, is possible. Are astronomers seriously considering and researching this phenomenon? What could be the signature of wormholes? Would next generations telescopes as ELT able to detect such signatures?

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Spending 5 minutes looking on ADS you can find some papers where observational signatures of wormholes are discussed, as for example this one. –  MBR Sep 30 '13 at 14:36
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This has been considered long ago (Here's a paper talking about this).

Wormholes are not forbidden by physics, but the creation of wormholes is iffy ground. THere are two possible paths one can take to create a wormhole:

  • Choose a pre-existing wormhole in the quantum foam and "expand" it by feeding it exotic matter.
  • "Tear and sew up" space — we're not sure if this is allowed by physics, as it ventures into the area of physics that we don't have an adequate explanation for.

Whatever it is, the creation and sustenance of a wormhole requires us to have control over exotic matter (in this case, particles/waves with negative mass/energy density). Vacuum fluctuations already have regions of negative energy density, but they're an uncontrollable quantum phenomenon by current technology.

"Faster than light travel" is a different matter, though. While wormholes let one jump to another point in space, one does not attain a speed greater than c whilst in them.

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