Quanta magazine has an interesting new piece up, an interview of Witten by Natalie Wolchover.
One topic covered in the interview is the question discussed in a recent posting, that of whether a different formulation of QFT exists, one not based on a choice of Lagrangian. Here Witten is non-committal, leaning to the idea such a thing might exist only in special cases:
Now, Nati Seiberg [a theoretical physicist who works down the hall] would possibly tell you that he has faith that there’s a better formulation of quantum field theory that we don’t know about that would make everything clearer. I’m not sure how much you should expect that to exist. That would be a dream, but it might be too much to hope for; I really don’t know…
I find it hard to believe there’s a new formulation that’s universal. I think it’s too much to hope for. I could point to theories where the standard approach really seems inadequate, so at least for those classes of quantum field theories, you could hope for a new formulation. But I really can’t imagine what it would be.
The standard example of where such a formulation might be needed is the 6d superconformal (2,0) theory, about which Witten says:
From the (2,0) theory’s existence and main properties, you can deduce an incredible amount about what happens in lower dimensions. An awful lot of important dualities in four and fewer dimensions follow from this six-dimensional theory and its properties. However, whereas what we know about quantum field theory is normally from quantizing a classical field theory, there’s no reasonable classical starting point of the (2,0) theory.
About the current state of M-theory, there’s this exchange:
You proposed M-theory 22 years ago. What are its prospects today?
Personally, I thought it was extremely clear it existed 22 years ago, but the level of confidence has got to be much higher today because AdS/CFT has given us precise definitions, at least in AdS space-time geometries. I think our understanding of what it is, though, is still very hazy. AdS/CFT and whatever’s come from it is the main new perspective compared to 22 years ago, but I think it’s perfectly possible that AdS/CFT is only one side of a multifaceted story. There might be other equally important facets.
What’s an example of something else we might need?
Maybe a bulk description of the quantum properties of space-time itself, rather than a holographic boundary description. There hasn’t been much progress in a long time in getting a better bulk description. And I think that might be because the answer is of a different kind than anything we’re used to. That would be my guess.
Are you willing to speculate about how it would be different?
I really doubt I can say anything useful. I guess I suspect that there’s an extra layer of abstractness compared to what we’re used to. I tend to think that there isn’t a precise quantum description of space-time — except in the types of situations where we know that there is, such as in AdS space. I tend to think, otherwise, things are a little bit murkier than an exact quantum description. But I can’t say anything useful.
The hope of 22 years ago was that it was non-perturbative string theory which would provide the desired “description of the quantum properties of space-time itself”. Over the years though studies of gauge-gravity duality have moved away from the use of string theory to provide this bulk description. Witten’s take on the current situation: “There hasn’t been much progress in a long time in getting a better bulk description. And I think that might be because the answer is of a different kind than anything we’re used to.” seems reasonable.
It’s interesting to hear that Witten was going back to Wheeler to see if he had any inspiration to offer the current “It from Qubit” program. This requires a patience for the “vague but inspirational” that Witten has more of these days than he used to:
Why do you have more patience for such things now?
I think when I was younger I always thought the next thing I did might be the best thing in my life. But at this point in life I’m less persuaded of that. If I waste a little time reading somebody’s essay, it doesn’t seem that bad.
This patience is not infinite though: among Witten’s many admirable qualities are the way he responds to:
Do you have any ideas about the meaning of existence?