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David B. Kaplan:
Research page
Complete
publications
Top-cited
papers
Research
Highlights (roughly chronological):
The
Composite Higgs Mechanism
My Ph.D. thesis
consisted of papers written with my advisor, Howard Georgi, on
a theory of the Higgs boson as a composite
particle, a relativistic bound state of
fermions. One motivation was that there
has never been any direct evidence in Nature
for a fundamental spin zero particle.
Furthermore, such particles suffer from
theoretical problems. Our theory, in
which the Higgs is a pseudo-Goldstone boson,
differs significantly from technicolor, and
provides an analytically tractable calculation
of Higgs boson properties. Our
idea recently led to a fascinating class of
theories called "Little
Higgs Theories", which will be testable
at the LHC. These theories
also employ "partial compositeness", a
novel way for generating fermion masses that I
introduced in "Flavor
at
SSC
Energies: A New Mechanism for Dynamically
Generated Fermion Masses", where quarks
get there masses by mixing with heavy
composite states, rather than coupling
directly to the Higgs. The title is sadly
inappropriate: the SSC was a collider planned
at the time to be more powerful than the LHC
and to be finished a decade earlier, but
subsequently cancelled by Congess after
investing $2 billion and countless human-years
of effort.
Kaon
Condensation
Shortly after
graduation, Ann
Nelson and I introduced the theory of
kaon condensation. By examining the
interactions between anti-kaons and nucleons
in chiral perturbation theory, we showed that
the binding energy of an anti-kaon in the core
of a neutron star could easily be in the
hundreds of MeV (at the time, this was an
order of magnitude larger than people
expected). This opens up the possibility
that the K- might
Bose-Einstein condense in dense matter at
densities as low as ~3 times nuclear
density. We also showed that similar
interactions could lead to a disoriented
chiral condensate in a heavy ion collision,
leading to enhanced kaon pair production; our
analysis preceded the discussion of DCC's for
pions. While our results suggested
new qualitative behavior for anti-kaons in
matter, they are not quantitatively reliable
as the analysis relied on the breakdown of
chiral perturbation theory due to a large
strange quark mass. There is vast literature
trying to pin down the anti-kaon/nucleon
interaction quantitatively in dense matter.
Prior to our work, it was generally believed
that there might be at most O(10) MeV
attraction, not the O(100) MeV attraction we
predicted; a recent
analysis of kaonic atoms confirms our
prediction that there is a very strong
attractive interaction between nuclear matter
and the anti-kaons. The same paper analyzes
Sigma hyperon atoms, and concludes that the
negatively charged Sigma hyperon is repelled
from nuclear matter. This is another
datum that favors kaon condensation, since the
Sigma
hyperon was a possible competitor for
introducing strange quarks into neutron
matter. What we need: a way to study dense
matter in lattice QCD!
Curiously, I
returned to kaon condensation many years later
in a different context: CFL
(color-flavor-locked) quark matter. Here
the issue was that CFL is the ground state
only when one assumes the quark masses to be
degenerate. In the real world, with a
heavy strange quark, the ground state wants to
get rid of some excess strange quarks.
Bedaque and Schaefer showed that the mechanism
is through kaon condensation (here the K0,
not the K-), and with S. Reddy I
explored this further in two
papers.
Strange
Matrix Elements
As a post-doc,
I proposed with A. Manohar that one could
access strange matrix elements in the proton
through neutral current experiments, both
parity violating electron scattering, and
elastic neutrino scattering. This paper
invented the notion of strange magnetic
moment and strangeness radius for the nucleon,
and both were subsequently explored by a
series of beautiful experiments, SAMPLE
and HAPPEX.
It was my work in a previous paper on axion-matter
interactions, where I used existing
(poor) neutrino elastic scattering data to
estimate strange matrix elements that made me
realize the potential of this approach.
Asymmetric dark
matter
It is very curious how the dark matter and
ordinary matter abundances in the universe are
different, but not hugely so. In a
little paper (which I am fond of) I introduced
the theory for what is known today as
"asymmetric dark matter", where the dark
matter and ordinary matter are cogenerated
subject to an overall conservation law, the
result being that the ratio of the two
densities arises roughly as the ratio of the
weak interaction scale to the strong
interaction scale.
Electroweak
baryogenesis
The excess of
matter over antimatter in the Universe is
ample indication that there is a lot of
physics beyond the standard model. In
particular, there needs to be baryon number
violation, new sources of CP violation, and a
cosmological epoch during which the Universe
was out of thermal equilibrium. The
original candidate for this epoch was the
Grand Unification Scale, although that runs
into some difficulties with cosmic
inflation. Another possibility is
that baryogenesis occurs at the electroweak
phase transition, there the baryon violation
occurs due to the electroweak anomaly, and new
sources of CP violation could exist. A
key requirement for this scenario is that the
phase transition be first order, to account
for the departure from thermal
equilibrium. These ideas existed in a
landmark paper by Kuzmin,
Rubakov and Shaposhnikov (1985), but my
work with A.
Cohen and A.
Nelson, provided the first detailed
scenario for how the baryon asymmetry could be
created during the electroweak phase
transition. In particular, our work
revealed the critical role of nonequilibrium
charge transport phenomena in electroweak
baryogenesis.
Chiral
fermions
on
the
lattice
I became
interested in understanding lattice fermions
when in 1981 I was touring possible graduate
schools, and at Princeton David
Gross explained the problem to me and
his thoughts on the matter. At issue is
whether it is possible to construct a lattice
field theory for fermions with chiral
symmetry; the problem was pressing because
chiral symmetry plays a critical role in
Standard Model (which has exact chiral
symmetries), and QCD (where chiral symmetries
are approximate, but which play a crucial role
in both the UV structure of the theory and the
IR phenomenology). I never liked the standard
theorems on the impossibility of having
fermions without doublers; what made most
sense to me was the less rigorous but more
physical argument based on anomalies: a chiral
theory has anomalies in the continuum, while a
lattice theory with a finite number of degrees
of freedom can have no anomalies --- ergo
chiral symmetry cannot be exact on the
lattice. In 1984 Zumino,
Wu & Zee explained how anomalies
were related in different dimensions, which
was followed by a beautiful paper by Callan
and Harvey on anomalous flow of charge
on and off topological defects. I was
intrigued by how chiral anomalies in four
dimensions could be understood from a
five-dimensional perspective -- where
chirality doesn't exist! This seemed
like a perfect fit for lattice field theory,
where one needed to break chiral symmetry, and
yet wanted to reproduce anomalies in the
continuum. Eventually this led to my
work on domain wall fermions, which are now a
widely used in lattice QCD calculations, and
which inspired Neuberger
and Narayanan's work on the overlap
operator -- the four dimensional effective
theory for domain wall fermions.
Currently among the top-cited
hep-lat papers five out of the
top ten are an outgrowth of my domain
wall fermion work.
Nuclear
physics
in
large-N
QCD
An expansion
ion the number of colors of QCD was introduced
by 't Hooft in the 1970's, and proved a useful
tool for meson and baryon
properties. Following a brief
discussion by Witten, I became interested in
understanding how nucleons interact in such an
expansion. My work with M. Savage
clarified how the I=J rule comes about for
baryon interactions in the large-N limit, and
with A. Manohar I classified the N-dependence
of the various terms in the nucleon-nucleon
potential. A comparison with
phenomenological models gave clear indication
of the same patterns predicted in large-N,
somewhat to my surprise and pleasure.
Natural
supersymmetry?
An important raison d'etre
for the Minimal Supersymmetric Standard Model
(MSSM) is to cure the naturalness problems in
the standard model...but with the present
bounds on supersymmetric particles and
associated symmetry violations, the MSSM is no
longer natural itself! This work comes
up with a general framework for a
supersymmetric alternative to the MSSM which
is more natural, and which has implications
for B physics and LHC phenomenology...in fact,
as the LHC improves limits on MSSM sparticles,
theis theory is looking increasingly
attractive.
Nuclear Effective
Theory
Effective
field
theory allows one to construct a
phenomenological theory of nucleon
interactions with a systematic expansion in
momentum. In a series of papers, my
collaborators M. Savage and M. Wise and I
introduced renormalization group concepts to
the subject, and were the first to suggest the
unitary fermions -- fermions with infinite
two-body scattering length -- were the
appropriate limit about which to construct an
effective theory for nuclear physics.
Our work stimulated my colleague George
Bertsch to issue his famous challenge to
theorists to come to a better understanding of
the many-body physics of unitary fermions, and
since then the study of such systems has
received a lot of attention in the
mnay-body/nuclear theory community, spurred on
by advances in atomic physics which creation
of such systems. The effective theory we
devised is a powerful extension of the old
effective range expansion to low energy
radiative and inelastic properties, such as
deuteron breakup and form factors, Compton
scattering, etc. A key advantage of the
EFT approach is the systematic inclusion of
short distance physics in an expansion of the
momenta of the process being considered, times
the range of the short distance
interaction. A beautiful application of
EFT techniques to a low energy nuclear process
is the state-of-the-art analysis of radiative
capture for Big-Bang nucleosynthesis by
Gautam Rupak.
Lattice
supersymmetry
Lattice field
theory for many years was thought to be
inconsistent with supersymmetry. The
problem is that in the UV, a lattice theory
cannot be supersymmetric any more than it can
be Lorentz invariant. This was
regretable, since much is known or postulated
about various strongly-coupled supersymmetric
gauge theories which would be interesting to
explore numerically. Of particular
interest is the connections discovered in the
1990's between supersymmetric gauge theories
and quantum gravity. The problem is
how to arrange an action so that supersymmetry
arises naturally in the infrared, even though
the UV theory is less symmetric. My own
interest stemmed from my first publication as
a graduate student in 1984, when I realized
that supersymmetry could arise as an
accidental symmetry in the form of N=1 Super
Yang-Mills theory, provided that
the particle content of the effective theory
consisted of a gauge boson and an adjoint Weyl
fermion, and that there existed a global
chiral symmetry preventing a fermion mass
(this preceded the similar observation by Curci
and Veneziano by several years). Quite a
few years later, my former student M.
Schmaltz and I showed how to exploit
this observation on the lattice with domain
wall fermions. In my first paper I had
speculated on the difficulty of obtaining
supersymmetric theories with scalars to arise
naturally in the infrared without having
supersymmetry in the UV. The key to how
to accomplish that trick eventually came from
string theory and deconstruction. Using these
techniques, in a series of papers with various
combinations of collaborators M. Unsal, M.
Endres, A. Cohen and E. Katz, we were
the first to show how one can latticize
certain supersymmetric gauge theories while
leaving intact an exact subset of the target
theory supercharges. While not very practical
now, I hope that in time this work will lead
to numerical investigations of quantum gravity
or supergravity.
Axions
Axions are particles associated with the
Peccei-Quinn mechanism for solving the strong CP
problem. They are also interesting candidates
for the dark matter. I have written a number of
papers about their couplings and
properties. My most recent (with Ann
Nelson) is about axions with very large decay
constant f,
say around the GUT scale. Such axions only
make sense in an inflationary universe, and then
only by having extremely small misalignment
between the axion field in the early universe,
and the value preferred by QCD. This
fine-tuning can be explained invoking the
anthropic principle --- it is actually the only
case I know of where the anthropic principle
really makes sense: one knows the a priori distribution
of
initial
axion
field values (a/f
being a random angle), and one knows that a
Universe without a particularly small range of
values for a/f
would not support habitable galaxies. With
inflation all initial values for a/f occur
somewhere, and we live in the only part of the
Universe where we could live: where the
galaxies are! In my paper with Ann we
discuss how there might be observable
consequences in this scenario (if we are
lucky): the fine tuning of a/f makes
us extremely sensitive to spatial variations in
a/f, and it turns out the existence of a cosmic
axion string as much as 1,000,000 time farther
away than our cosmic horizon could be seen as a
difference between our peculiar velocities
relative to the CMB, and relative to distant
type I supernovas. Seeing this effect
would be a stunning window into the
pre-inflationary Universe!
Biophysics
Identical proteins will join up to form
complexes, and empirically these complexes are
more often than not symmetric. Why is
that? David Baker and collaborators had
the picture that in a random arrangment, the
system would have N interactions of gaussian
randomly distributed strength, while the
symmetric arrangement would have N/2 pairs of
identical random interactions. The latter
would have a larger variance, and so on
the tail of the distribution, would have a
greater chance of being strongly
attractive. This would allow for a larger
population of symmetric complexes to be acted on
by evolutionary pressures, giving rise to the
predominantly symmetric populations found today
with a biological role to play. My role in
the paper "Emergence
of
symmetry
in
homooligomeric biological assemblies" was
to figure out the geometric probability
distribution for different relative
orientations.
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