Address/Telephone:
Institute for Nuclear Theory
Box 351550
University of Washington
Seattle WA 98195-1550 USA
(206) 685-3546
email: dbkaplan
Links:
David's home page
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David B.
Kaplan: Research page
Complete
publications
Most
cited papers
Research
Highlights (roughly reverse chronological):
Sign problems, noise, and quantum computing
One of the hardest and most important unsolved
problems of the Standard Model is how to connect
QCD -- the theory of the strong interactions --
to the actual properties of matter. This
is a nonperturbative problem, presumably
requiring lattice QCD, yet lattice QCD is not
computationally tractable when there are a
significant number of quarks present, due to a
severe sign problem in the path integral which
renders calculations impossibly noisy. In
the earlier three of these papers with
collaborators I have taken a few baby steps to
understand the problem by studying the spectrum
and origin of the noise one encounters.
This work points to the need to formulate QCD
not just in terms of quarks and gluons, but also
with fundamental pion fields -- although it
remains unsolved how to do this. The most recent
of my papers looks instead at completely
abandoning the conventional paradigm of
scientific computation, turning instead to
quantum computers. The advantage of
quantum computers is the vast Hilbert space they
operate in with a modest number of qubits, which
has been shown in various cases to allow
exponential speed up of computations, compared
to classicalcomputers. In the paper Ground
States via Spectral Combing my
collaborators and I propose a new quantum
algorithm for efficiently finding the ground
state of a many-body system which has some
promising features.
Chiral
fermions
and
chiral gauge theories on
the lattice
This is a major
recurring theme in my research. I became
interested in the problem of how to define
lattice fermions with chiral symmetry 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. The problem
was pressing because chiral symmetry plays a
critical role in the Standard Model (which has
exact local 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 --- implying that 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, in which
four-dimensional chiral fermions appear as
surface modes of a five dimensional
lattice. A key feature of the theory is
the topological nature of these surface modes,
as explained in a paper
written in collaboration with Golterman and
Jansen. Domain wall fermions, and their
cousin the overlap fermion, are now widely
used in lattice QCD simulations where chiral
symmetry is important, and these
topological surface mode fermions have
appeared recently in the condensed matter
literature, in the discussion of topological
insulators, which are essentially the same
physics. For example, Majorana zeromodes which
were first introduced to study lattice
supersymmetry are now discussed as
candidates for topological quantum computing;
and the model by Kane and Mele for the Quantum
Spin Hall Effect was considered over a decade
earlier as the simplest prototype for
constructing chiral gauge theories, where the
Callan-Harvey current in the bulk does not
carry gauge charges, so that the chiral
zeromodes are independently free of chiral
gauge anomalies at each surface. Most
recently I have returned to such theories for
constructing lattice models of chiral gauge
theories. This
work suggests that the Standard Model
could possess ghostly mirror fermions which
interact with our world only through
topologically nontrivial gauge field
configurations.
Flavor
physics at a TeV
Recently I have been thinking about a class of
theories of flavor that could have new flavor
physics at the several TeV scale without running
afoul of experimental limits on flavor changing
neutral currents. Such theories are
exciting because they have new flavor physics at
low enough energy that some parts of the theory
might be testable at the LHC. This work is an
outgrowth of Composite Higgs and Little Higgs
theories.
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
regrettable, 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, an idea
proposed by Arkani-Hamed, Cohen and Georgi.
Using these techniques, in a series of papers
with various combinations of collaborators M.
Unsal, M. Endres, A. Cohen and E. Katz,
we were able 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.
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, arguing that the unitary fermion
limit (fermions with infinite two-body
scattering length) were the appropriate point
about which to construct an effective theory
expansion 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. Sadly, the theory did not
do so well about the pion mass scale due to
properties of the tensor force. Since
then there has been a large amount of work on
chiral effective nuclear forces, but I am not
satisfied with the theoretical foundations
under this work, and believe that new ideas
are needed.
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 arrangement, 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 (minor) role
in the paper "Emergence
of
symmetry
in
homooligomeric biological assemblies" was
to figure out the geometric probability
distribution for different relative
orientations.
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 Martin
Savage clarified how the I=J rule comes
about for baryon interactions in the large-N
limit, and Aneesh Manohar and 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 surprisingly.
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 very 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,
this theory (known as "Effective
Supersymmetry" or "Natural Supersymmetry") is
looking increasingly attractive.
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); my work
with A.
Cohen and A.
Nelson, provided a 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.
My co-authors went on to write the
first paper explaining how this could
work in supersymmetric theories.
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
Single Explanation for Both the Baryon and
Dark Matter Densities I discussed
a possible explanation for why this is not a
coincidence, in an approach 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.
Strange
Matrix Elements
As a post-doc,
my work on axion-matter
interactions lead me to propose that the
strangeness content of the proton could be
accessed by neutral current experiments using
elastic neutrino-proton scattering. This
was developed further in a paper with A.
Manohar where we considered parity violating
electron scattering as well. In that
paper we invented the notion of a
strange magnetic moment and a strangeness
radius for the nucleon, and both were
subsequently explored by a series of beautiful
experiments, SAMPLE
and HAPPEX,
although both experiments found rather small
strange quark contributions.
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!
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, an order of magnitude larger
than people expected at the time. 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. 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; analysis
of kaonic atoms seems to confirm our
prediction that there is a very strong
attractive interaction between nuclear matter
and the anti-kaons. That 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!
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 Schäfer showed
that the mechanism is through kaon condensation
(here the K0, not the K-),
and with Sanjay
Reddy I explored this further in two
papers.
The
Composite Higgs and quarks
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. This idea has
been developed further by other authors in a
fascinating class of theories called "Little
Higgs Theories", which will be testable
at the LHC. I have also worked on the idea
that quarks and leptons might have
substructure. The idea of "partial
compositeness" was introduced in "Flavor
at
SSC
Energies: A New Mechanism for Dynamically
Generated Fermion Masses", a mechanism
whereby quarks and leptons get there masses by
mixing with heavy composite states -- similar
to the proton, but heavier -- rather than by
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 Congress after
investing $2 billion and countless human-years
of effort.) Another idea for explaining
quark substructure in Flavor
from Strongly Coupled Supersymmetry,
written with my students Martin
Schmaltz and François LePeintre, is that
the three families might have internal
structure like three isotopes of an element
--- but in this case, where the lighter
families have more constituents than the
heavier ones. I suspect that the AdS/CFT
dual of such a theory might look similar to
the picture described in my recent paper with
my student Sichun Sun, where spacetime behaves
like a topological
insulator with a massless surface mode
corresponding to each generation of fermion.
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