Two-dimensional conformal field theories and their moduli space.

Rutgers University New Brunswick, New Brunswick NJ

Investigators

Abstract

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). In the last few years, Huang has proved the Verlinde conjecture and the Verlinde formula which play a fundamental role in Conformal Field Theory and related subjects and has proved the rigidity and modularity of the ribbon category of modules for vertex operator algebras satisfying certain natural conditions. He has investigated other problems in the mathematical foundation of two-dimensional conformal field theory. His interest is in tackling some of the still-unsolved hard problems in that field. The proposed research of Huang is expected to give results on general orbifold conformal field theories and higher-genus conformal field theories, a mathematical understanding of the connection between certain orbifold conformal field theories and certain Calabi-Yau manifolds, a solid foundation to a mathematical theory of deformations of conformal field theories, a better understanding of the geometry of Calabi-Yau manifolds related to conformal field theories and new insight into the mathematics underlying problems in physics. Broader impacts arise from the PI's teaching, mentoring, advising, lecturing, expository writing, conference-organizing, seminar-organizing, volume-editing and other such activities. In particular, he will continue to devote a large amount of time to train REU undergraduate students and Ph.D. students. Huang will continue to encourage the participation of women and members of underrepresented minority groups in their areas of study. Besides studying the theoretical aspects of two-dimensional conformal field theory, Huang is also interested in finding applications of his results and approaches to problems in physics, such as problems related to quantum computing and string theory.