Collaborative Research: Geometry, Entanglement and the Dynamics of Fields, Strings and Gravity

This Collaborative Grant supports the research of Professors Sebastian Franco, Parameswaran Nair and Alexios Polychronakos at the City College of the City University of New York and Professors Daniel Kabat and Dimitra Karabali at Lehman College of the City University of New York. As part of this research project, the PIs will advance our understanding of the physical world at its most fundamental level by bringing new mathematical tools to bear on some of nature's most puzzling properties. One property, arising from the quantum world, is known as "quantum entanglement". Quantum entanglement means that two well-separated systems need not have independent properties of their own. This surprising aspect of nature --- at least in principle --- enables quantum computers to outrace any ordinary computer. Another property crucial to modern astronomy and cosmology is Einstein's insight that gravity is related to the curvature of space and time. This research relates and unifies these concepts by establishing connections between them and by developing new mathematical tools through which to study their properties. This exploration will take place within quantum field theory, the fundamental framework for describing all known particle interactions, and within string theory, the most promising direction for a full unification of the quantum world with gravity. This research will advance the national interest by maintaining US preeminence in the exploration and understanding of physical laws. This project will also involve graduate students, thereby providing crucial research training for young scientists. Undergraduate and high school students will also be integrated into the research, further broadening the societal impact of this project. More technically, this project draws on mathematical concepts from geometry, abstract algebra, and quantum information theory to build new understandings of field theory, string theory, and gravity. Specific areas of research include: I) strongly interacting gauge fields, which form the paradigm for nuclear forces; II) the role of boundary effects on quantum entanglement; III) geometric approaches to the quantum Hall effect, a phenomenon of central importance in low temperature condensed matter systems; IV) braneworld dynamics, focusing on phenomenology and cosmology with broken Lorentz invariance; V) chaos and thermalization in multi-matrix models and on non-commutative spaces; VI) brane constructions of supersymmetric field theories, emphasizing models with (0,2) supersymmetry and counts of BPS states; VII) stringy realizations of superconformal field theories in 5D; VIII) statistical mechanics of random walk processes; and IX) statistical mechanics of magnetic systems with higher unitary symmetry. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.