<--
.. title: Your Week in Seminars: Conformal Edition
.. date: 2010-11-01 17:58:00
.. tags:
.. category: old
.. slug: your-week-in-seminars-conformal-edition
.. author: Yariv
-->
Another week has gone by here in Cornell. The last leaves are turning
red, a hint of snow passed us on the weekend, and the undergrads have
hit the streets and parties in minimal clothing, then did the same again
next day wearing a set of cat ears. And in the physics department, we
had the usual three talks. On Monday, the colloquium speaker was Holger
MÃ¼ller from UC Berkeley, talking about Gravitational Redshift,
Equivalence Principle, and Matter Waves. The center of the talk was
Muller's experimental device, an atom interferometer. Many of you will
remember the Michelson-Morley interferometer, the device used to
disprove the existence of the ether. A light-interferometer essentially
takes a beam of light, splits it in two and then merges it back again,
using the result of the interference between the two parts to learn
something about the relative difference between the optical paths taken
by the two. The atom interferometer, then, performs a similar function
with atom wavefunctions. An atom is shot up into the air and a laser is
directed towards it and calibrated to interact with the atom half the
time. The atom's wavefunction is split two trajectories, at the end of
which another laser is calibrated to bring the two paths back together.
The detector can then measure the path difference between the two
trajectories, and as we have excellent ways of measuring time and the
mass and energy of the atom, this amounts to a very accurate measurement
of g, the free-fall constant. Muller went on to show how his team has
been using the interferometer to perform very accurate measurements of
General Relativity, from its isotropy to the universality of free fall
motion for objects of different masses. There were some neat tricks
described, and they mentioned the ability to measure those [minute
differences](http://thevirtuosi.blogspot.com/2010/09/microseconds-and-miles_7470.html)
in gravity experienced by moving the system one meter upwards. It's
always a little difficult to get excited about tests that confirm an
accepted theory, especially one like General Relativity, but I think
this is important work. To paraphrase the words of fellow Virtuos Jared,
GR is always going to be right up until we find where it breaks. On
Wednesday, David Kaplan talked about Conformality Lost. This talk was
about QCD, but not about QCD. One of the features of QCD, or really
field theories in general, is the running of the coupling constants.
Where in classical theories the strength of the interaction between two
particles is constant and depends only on the distance between them,
field theory shows us how the strength of the interaction changes with
the energy of the participating particles. This is crucial, for
instance, for theories of grand unification that posit that the known
forces are all the same at very high energies. In QCD, in particular,
the running of the constant also has to with confinement and asymptotic
freedom. Confinement is the notion that quarks can never break free of
each other, and so we never observe them alone in nature, only within
particles such as protons, neutrons, baryons and mesons. Asymptotic
freedom is the notion that at high energies, if we collide another
particle with a quark, it behaves as if it was free of other influence.
If we associate long distances with low energy and short distances with
high energy, we can see how the coupling must flow from very small at
one end to very large at the other end. One of the interesting things
about the running of the coupling is that it defines a scale for the
theory. If the coupling is different for particles of energy E~1~ and
E~2~, then we can choose some value of the coupling and describe our
energy in relation to the energy relative to this scale. Theories
without running coupling are called conformal and have no natural scale.
QCD, it seems, behave this way if you take it all the way to asymptotic
freedom. Kaplan talked about the investigation of this conformal stage
of the theory, its existence and inexistence. As an analog he showed a
quantum-mechanical system of a particle in a Coulombic, potential. The
minimum energy of this system is given by solution of a quadratic
equation, which can have either two solutions, one or none, depending on
the relation between the mass of the particle and the strength of the
potential. A scale exists in this case only if there are two solutions:
a single energy is meaningless, of course, because we can always add a
constant, but if there's two of them then the difference defines a
scale. This toy model, it turns out, can be analogous to a QCD with the
equivalent parameter being the relative number of flavors (kind of
particles) and colors (different charges in the theory, red, blue and
green in our regular QCD). There were a number of interesting results
from this model, the most exciting one, perhaps, being the possible
existence of a "mirror" QCD theory beyond the conformal point of QCD, a
sort of theory with a different number of colors and different gauge
groups. Kaplan ended his talk by talking of at least one possible
candidate for this mirror theory that they had recently found. Finally,
on Friday, we had Ami Katz from Boston University talk about CFT/AdS.
AdS/CFT has been a big buzzword for the last decade or so. The CFT here
stands for conformal field theory of the kind mentioned in the previous
summary, and AdS stands for Anti-de Sitter space, a geometry of
spacetime possible in general relativity. The slash in between stands
for a duality that allows results from one theory to be interpreted in
the other and vice versa. This has some exciting implications since it
allows us to use each theory in the regime where we can solve it.
Particle theorists are, in general, trying to use the CFT to solve for
high-energy theories that behave like AdS. Katz had apparently rewritten
the duality as CFT/AdS, to signal that he was asking the opposite
question, starting with a CFT and asking whether it is a good fit for
the duality. A large part of the talk was dedicated to making an analogy
from CFTs into conventional field theories. We know pretty well when a
field theory is a good description of reality and when it tends to break
down. This has to do, usually, with some cutoff energy, a scale at which
new physics comes into play. As long as we stay at energies far below
that cutoff, the effects of the unknown physics will be a small
correction to the calculations we make with our known physics. In CFTs,
we had just said, there is no energy scale, and so the question must be
different. The relevant question, apparently, is the dimensionality of
operators - not what their energy scale is, but how they scale with a
change of energy. For instance, a derivative behaves like inverse
distance, and distance behaves like inverse energy, so a single
derivative scales linearly in energy, while a double derivative scale
quadratically. I didn't understand much past the half-point of this
lecture, but the bottom line appeared to be that a well-behaved CFT has
a gap in its operators dimensionality, allowing us to focus on one
operator and plenty of its derivatives before coming to the scaling of
the next operator. This kind of gap allows our perturbative corrections
to remain perturbative when we go to the AdS side. That's it for last
week, with its conformal ups and down. As usual, we're past the first
seminar of the new week, which was non-wimpy talk about WIMPs. Still
ahead this week are superconductors (and more AdS/CFT, presumably) and
some non-thermal histories of the universe. (that is, of course, if I
don't freeze first - temperatures have dropped below zero already. It's
so much colder when you work in Celsius)