Perimeter Institute proposes a new research program in mathematical physics, with the goal of dramatically expanding our understanding of quantum field theories (QFTs). We invite the Templeton Foundation to support this program by providing partial funding for a new postdoctoral fellow and for two new annual workshops.

QFTs are at the root of much of modern physics, foundational to fields from high energy to condensed matter to cosmology. They are at the core of recent progress in quantum gravity and string theory. They have deep, mostly unexplored mathematical implications, and are opening new avenues of research among mathematicians.

There is new evidence that the QFTs we can currently define are only a tiny subset of all possible QFTs. This suggests a huge gap in our knowledge about something vital – and presents a great opportunity for progress. We need to embark on a full exploration of the uncharted territory that is the complete space of QFTs.

Revolutionary new ideas (including several from Perimeter researchers) offer new opportunities to pursue this goal. Nevertheless, it is a difficult project, and will require sophisticated, cross-disciplinary efforts, including the development of alternative computational schemes for gauge theory and the use of information-theoretic methods and holography. Perimeter is one of the few places with the expertise to do this.

If we can make progress in mapping the complete space of QFTs, the potential for enduring impact is high. Concrete outcomes will include scientific publications and presentations. We imagine progress toward better explaining recent results in high energy physics, or new abilities to tailor exotic quantum systems for practical applications. But beyond the practical, we imagine the richness of new phenomena awaiting us in the new theories. The ultimate goal of this project is to better understand the fundamental laws of the universe and to make deep mathematical advances.