x***u
发帖数: 6421 | 1 Could you explain the new "deconfined" quantum critical theory? | c****e
发帖数: 2097 | 2 hehe, far from an expert, but googled it :-)
it's a 2nd order phase trans., and it seems the field theory is rather
simple. i don't know the physics behind it.
also, i don't understand why it's a big deal:
the 'cft' at the transition point is not one of the L-G (minimal) models,
rather, it's a field carrying spin 1/2
coupled to a U(1) gauge field. and the field with spin seems to describe
a topological (defect) vortex, which becomes 'infinitely' thick and
tensionless at transition point.
suppos
【在 x***u 的大作中提到】
: Could you explain the new "deconfined" quantum critical theory?
| w****1
发帖数: 4931 | 3 As far as I understand the quantum critical theory is described by a CFT
that connects a Higgs phase to a Coulomb phase. It is described by the IR
fixed point of a (fined tuned) gauge theory rather than a Wilson-Fisher type
fixed point. "Simple" field theories are often the hardest to solve. Highly
supersymmetric field theories look complicated but are easy to solve.:)
【在 c****e 的大作中提到】
: hehe, far from an expert, but googled it :-)
: it's a 2nd order phase trans., and it seems the field theory is rather
: simple. i don't know the physics behind it.
: also, i don't understand why it's a big deal:
: the 'cft' at the transition point is not one of the L-G (minimal) models,
: rather, it's a field carrying spin 1/2
: coupled to a U(1) gauge field. and the field with spin seems to describe
: a topological (defect) vortex, which becomes 'infinitely' thick and
: tensionless at transition point.
: suppos
| c****e
发帖数: 2097 | 4 hmm. are you talking about the 'deconfined' q... c..? i see, indeed sachdev
has such a phase diagram. when i googled i found some slides by "Lentil"
soup explaining the more specific thing i was trying to read.
but sachdev's CP1 model looks so mundane, i can not suspect anything
interesting goingon in it.
and certainly this model is not a supersymmetric model, as he constantly
refers to through out starting in the abstract. it is certainly NOT the N=8
super yang-mills theory.
it's also NOT th
【在 w****1 的大作中提到】
: As far as I understand the quantum critical theory is described by a CFT
: that connects a Higgs phase to a Coulomb phase. It is described by the IR
: fixed point of a (fined tuned) gauge theory rather than a Wilson-Fisher type
: fixed point. "Simple" field theories are often the hardest to solve. Highly
: supersymmetric field theories look complicated but are easy to solve.:)
| w****1
发帖数: 4931 | 5 there are common features shared by strongly coupled CFTs, supersymmetric or
not. For instance, N=4 SYM vs QCD. It is not clear what are all the lessons
one can learn from the maximally supersymmetric models, but there are
definitely something to make out it, even if one is ultimately interested in
the purely bosonic theory.
sachdev
=8
【在 c****e 的大作中提到】
: hmm. are you talking about the 'deconfined' q... c..? i see, indeed sachdev
: has such a phase diagram. when i googled i found some slides by "Lentil"
: soup explaining the more specific thing i was trying to read.
: but sachdev's CP1 model looks so mundane, i can not suspect anything
: interesting goingon in it.
: and certainly this model is not a supersymmetric model, as he constantly
: refers to through out starting in the abstract. it is certainly NOT the N=8
: super yang-mills theory.
: it's also NOT th
| w****1
发帖数: 4931 | 6 By the way, N=8 SYM is only a UV description, which can be deceiving. The IR
dynamics may look very different. For instance, now we believe that the IR
CFT is described by a strongly coupled Chern-Simons-matter theory at CS
level k=1, which has no propagating gauge field. Of course, the
superconformal algebra is there and governs the spectrum and correlation
functions of certain operators in the CFT, so that tells you it's different
from the bosonic theory.
sachdev
=8
【在 c****e 的大作中提到】
: hmm. are you talking about the 'deconfined' q... c..? i see, indeed sachdev
: has such a phase diagram. when i googled i found some slides by "Lentil"
: soup explaining the more specific thing i was trying to read.
: but sachdev's CP1 model looks so mundane, i can not suspect anything
: interesting goingon in it.
: and certainly this model is not a supersymmetric model, as he constantly
: refers to through out starting in the abstract. it is certainly NOT the N=8
: super yang-mills theory.
: it's also NOT th
| c****e
发帖数: 2097 | 7 this was one of my points, the BL and other theory is now identified,
and certainly it's not looking like the CP^1 model.
and your other post: yeah, that could be true, for some quantities,
as argued by kovtun et.al (universality at finite T). but it can't be
true for the susy and non-susy theory to be really identical.
one can take the M2 story as some evidence against that.
the ads/cmt proposal seems utterly naive.
ok, i feel this is again going a bit off topic to the original
post. So maybe
【在 w****1 的大作中提到】
: By the way, N=8 SYM is only a UV description, which can be deceiving. The IR
: dynamics may look very different. For instance, now we believe that the IR
: CFT is described by a strongly coupled Chern-Simons-matter theory at CS
: level k=1, which has no propagating gauge field. Of course, the
: superconformal algebra is there and governs the spectrum and correlation
: functions of certain operators in the CFT, so that tells you it's different
: from the bosonic theory.
:
: sachdev
: =8
| w****1
发帖数: 4931 | 8 AdS/CFT has already taught us a lot about CFTs, regardless of whether you
buy it or not.
【在 c****e 的大作中提到】
: this was one of my points, the BL and other theory is now identified,
: and certainly it's not looking like the CP^1 model.
: and your other post: yeah, that could be true, for some quantities,
: as argued by kovtun et.al (universality at finite T). but it can't be
: true for the susy and non-susy theory to be really identical.
: one can take the M2 story as some evidence against that.
: the ads/cmt proposal seems utterly naive.
: ok, i feel this is again going a bit off topic to the original
: post. So maybe
| c****e
发帖数: 2097 | 9 I certainly agree with that, although how much over-promotion comes in
everyone has different opinion. and to its credit, these days it's roughly
the
only field active in string theory.
in the end though, it could fail to deliver.
and what have we learned about CFTs we didn't know without
AdS/CFT in terms of field theory? and why the many attempts
to derive it so far look very surely bound for failure?
it's not a belief system, is it?
having now over 5000+ citations doesn't mean it's gained stat
【在 w****1 的大作中提到】
: AdS/CFT has already taught us a lot about CFTs, regardless of whether you
: buy it or not.
| c****e
发帖数: 2097 | 10
plus, is it not true that for this correspondence to work literally, you
need a
large degrees of freedom in the CFT, see my earlier attempt in trying to
point
out a 'gravity' dual for the 2,3d Ising models would be hard to come by.
【在 w****1 的大作中提到】
: AdS/CFT has already taught us a lot about CFTs, regardless of whether you
: buy it or not.
| | | w****1
发帖数: 4931 | 11 Dude, if you tell me that AdS/CFT is the only active field in string theory,
then I could say that there is no active field in condensed matter theory.:)
Let me give one simple example of something we know from AdS/CFT about the
field theory, that is almost certainly true, but has not been possible to
derive directly using field theory techniques: the free energy of N=4 SYM at
finite temperature in the strong 't Hooft coupling limit. Note that the
cusp anomalous dimension at strong coupling has
【在 c****e 的大作中提到】
: I certainly agree with that, although how much over-promotion comes in
: everyone has different opinion. and to its credit, these days it's roughly
: the
: only field active in string theory.
: in the end though, it could fail to deliver.
: and what have we learned about CFTs we didn't know without
: AdS/CFT in terms of field theory? and why the many attempts
: to derive it so far look very surely bound for failure?
: it's not a belief system, is it?
: having now over 5000+ citations doesn't mean it's gained stat
| w****1
发帖数: 4931 | 12 That doesn't mean the duality is wrong -- it's just that we cannot solve
string theory in AdS at strong coupling. We talk about things we cannot
compute all the time, and I don't see why you feel so uncomfortable about it
.:) As I said, the only way you can hope to solve a strongly coupled system
analytically, is either the system has a weakly coupled dual description, or
the system is integrable for some reason.
In the 80s people would think that there is no way we could ever come up
with a non
【在 c****e 的大作中提到】
:
: plus, is it not true that for this correspondence to work literally, you
: need a
: large degrees of freedom in the CFT, see my earlier attempt in trying to
: point
: out a 'gravity' dual for the 2,3d Ising models would be hard to come by.
| c****e
发帖数: 2097 | 13
yeah, it also does not mean it's right. and it could be the case we don't
know
how to solve it, meaning one of a few things, such as not knowing how to
do curved OPEs, but it could also be that there's something rather
completely
new yet to come.
it
in this particular case, i'm uncomfortable not about the correspondence. it'
s
probably psychological,but i'm uncomfortable when not so convincing
conclusions are drawn. also that's still minor, but don't force me to
believe it.
system
or
as long as
【在 w****1 的大作中提到】
: That doesn't mean the duality is wrong -- it's just that we cannot solve
: string theory in AdS at strong coupling. We talk about things we cannot
: compute all the time, and I don't see why you feel so uncomfortable about it
: .:) As I said, the only way you can hope to solve a strongly coupled system
: analytically, is either the system has a weakly coupled dual description, or
: the system is integrable for some reason.
: In the 80s people would think that there is no way we could ever come up
: with a non
| c****e
发帖数: 2097 | 14
theory,
.:)
i really have no idea whether cmth is active these days. but they have
somewhat different orientation.
ok, string pheno is still alive.
if you are implying cmth people are picking up ads/cft to save some of their
causes, i don't know if that's true to large scale. in other words, is it
just us string theory people hoping so?
at
valid example, sugra/string give you the leading contributions which
probably can't be dealt with integrability as you mentioned, as susy
is not offering pr
【在 w****1 的大作中提到】
: Dude, if you tell me that AdS/CFT is the only active field in string theory,
: then I could say that there is no active field in condensed matter theory.:)
: Let me give one simple example of something we know from AdS/CFT about the
: field theory, that is almost certainly true, but has not been possible to
: derive directly using field theory techniques: the free energy of N=4 SYM at
: finite temperature in the strong 't Hooft coupling limit. Note that the
: cusp anomalous dimension at strong coupling has
| w****1
发帖数: 4931 | 15 Well, we used to think that the CFT dual of M-theory on AdS4xS7 is "blurred"
, and now we have ABJM -- which is still blurred at small CS level k, but at
least it is in principle well defined.
I wasn't implying that condensed matter theorists are picking up on ads/cft.
Once I complained to a condensed matter theorist that progress in string
theory is slow these days, and he says string theorists are too spoiled --
progress like ads/cft don't come by every year or even every decade.:)
their
【在 c****e 的大作中提到】
:
: theory,
: .:)
: i really have no idea whether cmth is active these days. but they have
: somewhat different orientation.
: ok, string pheno is still alive.
: if you are implying cmth people are picking up ads/cft to save some of their
: causes, i don't know if that's true to large scale. in other words, is it
: just us string theory people hoping so?
: at
| c****e
发帖数: 2097 | 16 ok, ABJM is really a hard theory to get a hold of. it looks very simple, but
that's kind of a deception.
considering the nature of cmth, probably nothing of this kind would have
been found there anyway.
slow is good for some people. when the pace is fast, it's hard to have time
to consider something for a long while. each coin has 2 sides, approximately.
blurred"
at
cft.
【在 w****1 的大作中提到】
: Well, we used to think that the CFT dual of M-theory on AdS4xS7 is "blurred"
: , and now we have ABJM -- which is still blurred at small CS level k, but at
: least it is in principle well defined.
: I wasn't implying that condensed matter theorists are picking up on ads/cft.
: Once I complained to a condensed matter theorist that progress in string
: theory is slow these days, and he says string theorists are too spoiled --
: progress like ads/cft don't come by every year or even every decade.:)
:
: their
| w****1
发帖数: 4931 | 17 Well it's not much harder than any other strongly coupled theories -- it's
probably a bit more complicated than N=4 SYM, even if it turns out to be
integrable.
but
time
approximately.
【在 c****e 的大作中提到】
: ok, ABJM is really a hard theory to get a hold of. it looks very simple, but
: that's kind of a deception.
: considering the nature of cmth, probably nothing of this kind would have
: been found there anyway.
: slow is good for some people. when the pace is fast, it's hard to have time
: to consider something for a long while. each coin has 2 sides, approximately.
:
: blurred"
: at
: cft.
| c****e
发帖数: 2097 | 18 yeah, sure. but the perturbative series in k is not presumably where
the new stuff would lie.
in YM you have a planar limit due to the existence of the g_YM
expansion, here if you would not like to expand w.r.t. to 1/k then
you're pretty much stuck.
sure that's expected, who said it should have a string dual except in
the large k limit.
【在 w****1 的大作中提到】
: Well it's not much harder than any other strongly coupled theories -- it's
: probably a bit more complicated than N=4 SYM, even if it turns out to be
: integrable.
:
: but
: time
: approximately.
| w****1
发帖数: 4931 | 19 You are dismissing it too easily. The new stuff lies in the 't Hooft limit
of ABJM theory as well. The k=1 theory is supposed to have N^{3/2} dof. That
's a bit hard to understand. What you could hope to understand, is the N^2 (
N/k)^{-1/2} dof in the 't Hooft limit at strong coupling N/k. While that by
itself we don't know how to derive from integrability, there are related
quantities that we may compute at strong coupling, such as cusp anomalous
dimension, which tells you about the radius the
【在 c****e 的大作中提到】
: yeah, sure. but the perturbative series in k is not presumably where
: the new stuff would lie.
: in YM you have a planar limit due to the existence of the g_YM
: expansion, here if you would not like to expand w.r.t. to 1/k then
: you're pretty much stuck.
: sure that's expected, who said it should have a string dual except in
: the large k limit.
| c****e
发帖数: 2097 | 20 i see, i did. i was more interested in thinking about the sense in which
the ABJM theory is an effective theory of say M2s, as the YM theories
were effective theories of strings.
That
(
by
【在 w****1 的大作中提到】
: You are dismissing it too easily. The new stuff lies in the 't Hooft limit
: of ABJM theory as well. The k=1 theory is supposed to have N^{3/2} dof. That
: 's a bit hard to understand. What you could hope to understand, is the N^2 (
: N/k)^{-1/2} dof in the 't Hooft limit at strong coupling N/k. While that by
: itself we don't know how to derive from integrability, there are related
: quantities that we may compute at strong coupling, such as cusp anomalous
: dimension, which tells you about the radius the
| | | w****1
发帖数: 4931 | 21 Well YM theories have coupling constants that can be made arbitrarily weak,
while the M2-branes don't. So the best you can hope for is to have a family
of theories that interpolate between, on one hand some weak coupling limit,
and on the other hand, M2-branes. ABJM does exactly this. And then you could
hope to learn about the strong coupling end (M2-branes) by extrapolating
from the weakly coupling regime. Integrability could help.
【在 c****e 的大作中提到】
: i see, i did. i was more interested in thinking about the sense in which
: the ABJM theory is an effective theory of say M2s, as the YM theories
: were effective theories of strings.
:
: That
: (
: by
| c****e
发帖数: 2097 | 22 how far could you extrapolate without running into new phases?
,
family
,
could
【在 w****1 的大作中提到】
: Well YM theories have coupling constants that can be made arbitrarily weak,
: while the M2-branes don't. So the best you can hope for is to have a family
: of theories that interpolate between, on one hand some weak coupling limit,
: and on the other hand, M2-branes. ABJM does exactly this. And then you could
: hope to learn about the strong coupling end (M2-branes) by extrapolating
: from the weakly coupling regime. Integrability could help.
| w****1
发帖数: 4931 | 23 Well that depends. RG is also a form of extrapolation, and it often does not
work very well, e.g. going from N=8 SYM in 3d to M2-branes. In ABJM, there
is potentially integrability, which may help.
The only parameter for the world volume theory of N M2-branes in flat space
is, well, N. And we already know the weakly coupled description in the large
N limit -- 11d supergravity on AdS4xS7. It is almost impossible to have two
equivalent "dual" descriptions both at weak coupling at the same time,
be
【在 c****e 的大作中提到】
: how far could you extrapolate without running into new phases?
:
: ,
: family
: ,
: could
|
|
