Originally Posted by

**sol invictus**
I'd say there's been a third "revolution" since then, the

AdS/CFT correspondence. ... In brief, the AdS/CFT duality is an explicit example of "holography" - it asserts that string theory on a certain spacetime background is exactly equivalent to a field theory in one less dimension.

Ah, many thanks, this is something of great interest I was unaware of. I am particularly intrigued by the requirement of a string theory on a spacetime background. It certainly seems that background dependence in string theory had been considered a weakness, at least up to now. Carlo Rovelli, in his book

*Quantum Gravity* (Cambridge University Press, 2004), asserts that quantum field theory discards the spacetime background altogether (e.g., "

*Thus, there is no background 'spacetime', forming the stage on which things move. There is no 'time' along which everything flows. The world in which we happen to live can be understood without using the notion of time.*" - page 31). He is not the only source indicating that quantum field theory (and string theory) can & should be background independent.

Now the AdS/CFT duality requires a string theory on a spacetime background, so this would appear to be indeed a "revolutionary" new direction to take things. But what about the equivalent field in one less dimension, is it background independent? If not, that would seem to be not just a departure from the norm for string theory, but a departure from the norm for quantum field theory in general.

At least that's the way it looks at first glance from where I sit. What are your thoughts on background independence and spacetime in quantum field theory?