Conformal Field Theories in Holography and String Theory

University Of Arizona, Tucson AZ

Investigators

Abstract

There are four fundamental forces in the universe. The electromagnetic force and the two nuclear forces are described by Quantum Field Theory (QFT); the gravitational force is described by the theory of General Relativity (GR). String Theory aims to unify these four forces, while at the same time providing a quantum mechanical description of gravity. In this endeavor, quantum field theories that are scale invariant, so called conformal field theories (CFTs), are crucial: On the one hand they describe how strings move and interact; on the other hand, through the principle of holography, they can describe quantum gravity. The PI aims to deepen the understanding of string theory and QFTs by investigating such CFTs and their applications, with a focus on their mathematical structure and their connection to mathematics. The work aims to construct new examples of CFTs that can be used in string theory. In addition, this project will have a broader impact on education by offering suitable activities and research projects for undergraduate and graduate students, thereby introducing them to contemporary research. The PI will also work with the Center for Recruitment and Retention of Mathematics Teachers at the University of Arizona to develop modules that introduce high school students to quantitative thinking and mathematical reasoning in physics and other STEM disciplines. At a more technical level, the PI will develop 2D conformal perturbation theory with a focus on orbifold CFTs. He will use this to investigate the interplay between rational and irrational CFTs in moduli spaces of Calabi-Yau sigma models, and to investigate how the spectrum of holographic 2D CFTs such as symmetric orbifolds changes over their moduli space. He will also construct new holographic CFTs using permutation orbifolds and lattice orbifolds, which may lead to new examples of AdS/CFT dualities. He will particularly focus on CFTs with sparse light spectrum and extremal or near extremal CFTs. This research will rely on recent results from mathematics such as the theory of non-abelian orbifolds of vertex operator algebras. 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.