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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.
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. A recent analysis of kaonic
atoms confirms 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.
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 existed 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
four out of five of the top-cited
hep-lat papers are an outgrowth of the domain wall fermion paper.
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.
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, as well as several techniques that made
power counting explicit, with applications to the deuteron. The
resulting theory 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.
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