Supersymmetric quantum field theory
We are interested in the classification and study of supersymmetric quantum field theories in a geometric framework. Starting from high-dimensional superstring/M-theory and putting them on specific non-compact geometric spaces, a large set of supersymmetric (superconformal) field theories can be constructed and their physical data can be computed geometrically. For example, 11d M-theory on complex threefold singularities gives rise to 5d N=1 superconformal field theories with non-trivial global symmetry. We hope to expand the existing classification of 5d N=1 theories and also proceed to lower dimensional cases.
String landscape of quantum gravity
String theory provides a natural way of constructing UV complete quantum gravity theories, which form a vast string landscape. Nonetheless, there also exists infinitely many low energy effective field theories that cannot be coupled to a UV complete quantum gravity theory, which form the "swampland". The precise boundary between the landscape and swampland is an important unsolved question. We wish to enlarge the known part of string landscape with new constructions in F/M-theory, and study their statistics. The results can also have indirect applications in beyond standard model physics and potential dark matter candidates.
Generalized symmetries in physics
Symmetry is a central concept in theoretical physics. In the recent years, various generalized notions of symmetry have been proposed and explored:
(1) Higher form symmetries;
(2) Higher group symmetries;
(3) Non-invertible symmetries;
(4) Other categorical symmetries.
We hope to obtain a better understanding of these generalized symmetries, and seek applications in both quantum field theory and lattice models.