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Kaplan photo

Institute for Nuclear Theory
Box 351550
University of Washington
Seattle WA 98195-1550 USA
(206) 685-3546
email: dbkaplan

David's home page


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.

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 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 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.