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I work directly in this field. This article covers a lot of a material that is at the forefront of theoretical high energy physics where we are neck-deep in the

I work directly in this field. This article covers a lot of a material that is at the forefront of theoretical high energy physics where we are neck-deep in the 'fog of war.' Truthfully, I can think of few subjects more difficult to describe to people not in the field than the conformal bootstrap; there are a lot of technical details that are easy to get hung up on but are crucial for understanding the big picture.

shepardrtc 9y ago
From the article, it looks very promising! Forgive me for my lack of understanding, but the article made it sound like it could supplant the notion of quarks and/or other elementary particles. Is that correct?
- eigenschwarz 9y ago
  Yes, not that they do exist but perhaps the notion of how a quantum field theory of quarks is really nearly the same thing in some ways as an Ising model, etc. The ultimate goal is to understand how these disparate physical systems are similarly mathematically structured and how to get from one to the next, and to find out the limits of the space of theories. (The signposts and roads analogy in the article is a good one.)
- auntienomen 9y ago
  That was Chew's original motivation, explaining the hadron/meson zoo without quarks and gluons, but it's not likely to happen any time soon. The conformal bootstrap program is about analyzing _conformal_ QFTs, those which look the same at every magnification setting. (The theory of hadrons is not conformal; if you zoom in, the particles get bigger.) In conformal QFTs, it turns out something like Chew's vision does hold. This implies a huge set of constraints, and it turns out you can use these constraints to find solutions to the equations of motion of these theories. This is a bit of a miracle, since it's extremely hard to solve these equations directly. It's also rather valuable, since conformal QFTs describe a lot of natural physical system (like the triple point phase of water). Being able to solve these theories with sufficiently good approximations means that you can compare theoretical and experimental predictions.
slewis 9y ago
Can you recommend some reading material, maybe a textbook, for folks who want to get into the details?
- aisofteng 9y ago
  That would take multiple textbooks and probably a couple years at minimum.
- eigenschwarz 9y ago
  Jared Kaplan, one of the researchers mentioned in the article, has a good set of notes here: http://sites.krieger.jhu.edu/jared-kaplan/files/2016/05/AdSCFTCourseNotesCurrentPublic.pdf http://sites.krieger.jhu.edu/jared-kaplan/files/2016/05/AdSC... David Tong does a good job explaining background physics and his notes can be found here: http://www.damtp.cam.ac.uk/user/tong/teaching.html http://www.damtp.cam.ac.uk/user/tong/teaching.html The fourth chapter of his string theory notes are about as approachable an introduction to conformal field theory that there is. His QFT notes are good too.
shostack 9y ago
Any chance you can attempt to ELI5 or ELI15 it?
- eigenschwarz 9y ago
  I'll give it a shot! Why are we interested in conformal field theories (CFTs)? One reason is it appears that all quantum field theories (QFTs) can be viewed as points along a “path” between a high-energy CFT to a low-energy CFT (c.f. the roadmap analogy in the article). Therefore, studying CFTs lets us study the space of well-defined QFTs, which are the mathematical framework in which to construct models in particle physics. At the same time, we can describe seemingly unrelated theories like the 3d Ising model as CFTs. The conformal bootstrap approach has enabled researchers to recently calculate the critical exponents for the 3d Ising model, which effectively “solves” the theory as the critical exponents are universal and characterize all the physical properties of a theory. The whole business about the “unknown polyhedron” and mapping “the geometry of theory space” means figuring out where these theories (e.g. Ising and other thing) live on this (higher-dimensional) map in relation to each other and potentially how to get from one to the other. The article briefly talks about the AdS/CFT or holographic principle and how we can use CFTs to study gravity (this is more what I'm interested in) but this is a whole other can of worms. Needless to say, it's also super exciting! Two examples of the types of 'big' questions being looked at are gravity as 'emerging' from a CFT and probing the black hole information paradox / beyond the horizon. Hope this helps!
- throwwit 9y ago
  Barrel of monkeys for physics math.
nabla9 9y ago
Out of curiosity, was Robert B. Laughlins (Nobel price for Laughlin wavefunction explaining the fractional quantum Hall effect) on right track and is his work any way relevant to what is currently happening? The Theory of Everything, R. B. Laughlin and David Pines http://www.pnas.org/content/97/1/28.full http://www.pnas.org/content/97/1/28.full A Different Universe: Reinventing Physics from the Bottom Down, R. B. Laughlin https://www.amazon.com/Different-Universe-Reinventing-Physics-Bottom/dp/0465038298 https://www.amazon.com/Different-Universe-Reinventing-Physic... http://large.stanford.edu/publications/ http://large.stanford.edu/publications/
- eigenschwarz 9y ago
  I'm not well-versed in his work but it seems like Laughlin is an advocate for the approaches to looking at the system instead of the components. One could say that is what the conformal bootstrap does when it's used to solve a theory by calculating its critical exponents. I'd definitely be interested in seeing if we could calculate the critical exponent of the IR fixed point of turbulence.
debt 9y ago
But like a Fourier transform is able to take something complex and express using simpler mathematical language. I would assume we could take something extremely abstract and explain it using simpler abstractions that more people could understand; similar to a Fourier transform.

shepardrtc 9y ago

From the article, it looks very promising! Forgive me for my lack of understanding, but the article made it sound like it could supplant the notion of quarks and/or other elementary particles. Is that correct?

eigenschwarz 9y ago
Yes, not that they do exist but perhaps the notion of how a quantum field theory of quarks is really nearly the same thing in some ways as an Ising model, etc. The ultimate goal is to understand how these disparate physical systems are similarly mathematically structured and how to get from one to the next, and to find out the limits of the space of theories. (The signposts and roads analogy in the article is a good one.)
auntienomen 9y ago
That was Chew's original motivation, explaining the hadron/meson zoo without quarks and gluons, but it's not likely to happen any time soon. The conformal bootstrap program is about analyzing _conformal_ QFTs, those which look the same at every magnification setting. (The theory of hadrons is not conformal; if you zoom in, the particles get bigger.) In conformal QFTs, it turns out something like Chew's vision does hold. This implies a huge set of constraints, and it turns out you can use these constraints to find solutions to the equations of motion of these theories. This is a bit of a miracle, since it's extremely hard to solve these equations directly. It's also rather valuable, since conformal QFTs describe a lot of natural physical system (like the triple point phase of water). Being able to solve these theories with sufficiently good approximations means that you can compare theoretical and experimental predictions.

slewis 9y ago

Can you recommend some reading material, maybe a textbook, for folks who want to get into the details?

aisofteng 9y ago
That would take multiple textbooks and probably a couple years at minimum.
eigenschwarz 9y ago
Jared Kaplan, one of the researchers mentioned in the article, has a good set of notes here: http://sites.krieger.jhu.edu/jared-kaplan/files/2016/05/AdSCFTCourseNotesCurrentPublic.pdf http://sites.krieger.jhu.edu/jared-kaplan/files/2016/05/AdSC... David Tong does a good job explaining background physics and his notes can be found here: http://www.damtp.cam.ac.uk/user/tong/teaching.html http://www.damtp.cam.ac.uk/user/tong/teaching.html The fourth chapter of his string theory notes are about as approachable an introduction to conformal field theory that there is. His QFT notes are good too.

shostack 9y ago

Any chance you can attempt to ELI5 or ELI15 it?

eigenschwarz 9y ago
I'll give it a shot! Why are we interested in conformal field theories (CFTs)? One reason is it appears that all quantum field theories (QFTs) can be viewed as points along a “path” between a high-energy CFT to a low-energy CFT (c.f. the roadmap analogy in the article). Therefore, studying CFTs lets us study the space of well-defined QFTs, which are the mathematical framework in which to construct models in particle physics. At the same time, we can describe seemingly unrelated theories like the 3d Ising model as CFTs. The conformal bootstrap approach has enabled researchers to recently calculate the critical exponents for the 3d Ising model, which effectively “solves” the theory as the critical exponents are universal and characterize all the physical properties of a theory. The whole business about the “unknown polyhedron” and mapping “the geometry of theory space” means figuring out where these theories (e.g. Ising and other thing) live on this (higher-dimensional) map in relation to each other and potentially how to get from one to the other. The article briefly talks about the AdS/CFT or holographic principle and how we can use CFTs to study gravity (this is more what I'm interested in) but this is a whole other can of worms. Needless to say, it's also super exciting! Two examples of the types of 'big' questions being looked at are gravity as 'emerging' from a CFT and probing the black hole information paradox / beyond the horizon. Hope this helps!
throwwit 9y ago
Barrel of monkeys for physics math.

nabla9 9y ago

Out of curiosity, was Robert B. Laughlins (Nobel price for Laughlin wavefunction explaining the fractional quantum Hall effect) on right track and is his work any way relevant to what is currently happening? The Theory of Everything, R. B. Laughlin and David Pines http://www.pnas.org/content/97/1/28.full http://www.pnas.org/content/97/1/28.full A Different Universe: Reinventing Physics from the Bottom Down, R. B. Laughlin https://www.amazon.com/Different-Universe-Reinventing-Physics-Bottom/dp/0465038298 https://www.amazon.com/Different-Universe-Reinventing-Physic... http://large.stanford.edu/publications/ http://large.stanford.edu/publications/

eigenschwarz 9y ago
I'm not well-versed in his work but it seems like Laughlin is an advocate for the approaches to looking at the system instead of the components. One could say that is what the conformal bootstrap does when it's used to solve a theory by calculating its critical exponents. I'd definitely be interested in seeing if we could calculate the critical exponent of the IR fixed point of turbulence.

debt 9y ago

But like a Fourier transform is able to take something complex and express using simpler mathematical language. I would assume we could take something extremely abstract and explain it using simpler abstractions that more people could understand; similar to a Fourier transform.