The Santa Barbara group proposes research on a broad spectrum of fundamental questions in Physics ranging from formal String Theory to calculating QCD matrix elements using Lattice Gauge Theory. They also propose applying field theory concepts to important problem in Biology such as RNA folding as well as using modern methods to understand Quantum Chaos. The proposed research in string theory will focus on fundamental questions in the formulation of the theory (including high energy scattering, time-dependent configurations, and holographic duality), possible observational signatures via cosmic superstrings, and the application of gauge/string duality to physics of gauge theories and other field theories. Related investigations include issues of scattering in gravitational theories, lessons from the black hole information paradox, and applications of models of emergent gravity to black hole physics. In particle physics and astrophysics, problems to be studied include the study of supersymmetric models, research to understand the smallness of the up quark mass and a proposal on how to solve the strong CP problem of QCD. There is also proposed a variety of studies in neutrino physics including studying the predictions for lepton masses in tetrahedral group models, CP violation in the lepton sector, and relations between neutrino and charged lepton masses. Research in quantum chaos theory will focus on the Ruelle resonances and their role in classical and quantum dynamics. Work in quantitative biology will continue the study of the topology of RNA folding using random matrix theory and Monte Carlo methods. Research in lattice gauge theory will be directed at the study of the masses of strongly interacting particles, the properties of light pseudoscalar mesons, the decays of particles with heavy quarks, the behavior of strongly interacting matter at high temperatures, and the generation of gauge configurations with improved staggered quarks for use by other lattice gauge theorists in their own research. The scientific broader impact of this proposal is that research in string theory is aimed at developing a unified theory of all of the fundamental interactions of nature. The proposed research in particle phenomenology and lattice gauge theory is directly related to, and supportive of, programs in experimental high energy physics. Furthermore, part of the effort in lattice gauge theory is aimed at developing large-scale computational infrastructure for the entire U.S. lattice gauge theory community. The approach being taken has broad possibilities for application to computationally-intensive problems in many areas of science and engineering. The research topics covered by this proposal provide excellent educational opportunities for students and postdocs. This educational role is also greatly strengthened by interactions with the many visitors to the Kavli Institute for Theoretical Physics (KITP).
The research supported by this grant covers a broad range of problem in high energy physics. Main areas of research are (a) the strong nuclear force, (b) the properties of various known or predicted elementary particles, (c) problems in the unification of general relativity and quantum mechanics, and (d) the relation between chaos, quantum mechanics, and thermodynamics. The strong nuclear force: The Standard Model is the set of theories which encompass our current understanding of the fundamental forces of nature. Quantum Chromodynamics (QCD) is the component of the Standard Model that describes the strong, or nuclear, forces. It identifies quarks as the fundamental building blocks of strongly interacting matter, and describes how they interact to form the sub-atomic world we observe. To extract many of the most interesting predictions of QCD requires large scale numerical simulations, which are recognized as one of the grand challenges of computational science. Under this grant, we have carried out simulations of QCD to determine some of the basic parameters of the Standard Model, to make precise tests of the Standard Model, and to search for phenomena which may require physical ideas that go beyond the Standard Model for their understanding. Among our most important results were determinations with unprecedented precision of the masses of the lightest quarks and the couplings of quarks to the weak interactions. We also carried outstudies of the equation of state of strongly interacting matterunder extreme conditions, such as those that existed in the early development of the universe and are created today in relativistic heavy-ion collision experiments. Elementary particles: (1) The discovery of the Higgs particle, which was theorized over 40 years ago to give mass to all the fundamental particles, was big news in 2012. We study the possibility that each quark and each lepton (for example the electron) has its own Higgs particle. (2) The mysterious neutrino, long thought to be exactly massless, has been discovered to have mass. We theorized about the origin of this puzzlingly small mass and study its impact about how matter came into existence in our universe. (3) The universe contains much more dark matter than the luminous matter known to us. We propose models of the nature of this dark matter. Quantum mechanics and general relativity: These two theories form the basis for our understanding of microscopic nature of matter, and the nature of spacetime. A major open question is to fit them together into a single unified theory of physics, but this faces a number of challenges. In particular, Stephen Hawking argued 40 years ago from a study of evaporating black holes that quantum mechanics must break down. His claim is now believed to be incorrect, based on arguments from string theory, but a complete theory of quantum black holes does not yet exist. During this grant, we showed that if quantum mechanics is fully correct, then spacetime must break down in an unexpected way: the event horizon of a black hole can't be the smooth space predicted by general relativity, but instead is a `firewall' of high energy particles. This conclusion is controversial, and has inspired many new ideas about the nature of quantum gravity. Black hole quantum mechanics also led to the discovery of the `holographic principle', which implies unexpected connections between gravity and the other forces. We have explored frameworks for making this principle more precise, and have applied it to a better understanding of the various forces, and of new states of matter. Other work tries to modify the theory of gravity in order to understand the dark energy that dominates the universe. Quantum chaos and thermodynamics: Work in this area investigated properties of quantum-mechanical systems whose classical counterparts exhibit chaotic motion. In particular, we investigated the relationship between quantum chaos and how large systems of many particles come to thermal equilibrium. This has very wide ranging implications, from the physics of cold atomic systems to black holes. Another particularly fascinating possibility is that the properties of a particular quantum chaotic system (that has yet to be found explicitly) could be used to verify the famous Riemann hypothesis about the distribution of prime numbers among the integers. We were able to find some specific properties that such a system must have; knowing these is an essential first step in its explicit construction. Other work: Included (1) application of mathematical methods to biological problems such as folding of RNA, (2) determining possible symmetries of quantum field theories, (3) studying possible methods of communication on cosmic scales using neutrinos and variable stars. PI’s on this grant have been active in writing textbooks on Einstein gravity, quantum field theory, and string theory, and communicating science to the public via lectures and a variety of media. Research training of postdocs, graduate students, and undergraduates was also an important function.
