MATRIX Research Program: New deformations of quantum field and gravity theories

The deep connections between mathematics, quantum field theory, and string theory (the latter being a leading candidate for a consistent framework to quantise gravity) have been for several decades a driving force of ground-breaking scientific discoveries in pure mathematics, mathematical physics, and theoretical physics. This program aims to bring together leading International and Australian experts in string theory and related topics with the goal of exchanging ideas, results, strengthening existing collaborations and launching new ones. The research focus is, broadly speaking, on deformations of quantum field and gravity theories that are related to string theory and mathematics. The program is developed around three key topics that are currently in the focus of international research:

(1) Marginal deformations in string theory and sigma-models;

(2) Higher-derivative deformations in string theory and supergravity;

(3) TTbar-like deformations of quantum field theories

There are rich interconnections amongst these topics, promising fruitful interactions and new discoveries. Recently, these have driven important developments, e.g., in the classifications of Calabi-Yau manifolds, non-planar/exact AdS/CFT and AdS supersymmetric black hole physics, generalised complex geometry and its extensions, 2D conformal or integrable field theories and their TTbar deformations, and many more. On the mathematical side, richness derives from the close connection of these topics with integrable systems, algebraic, differential and enumerative geometry, graded Lie algebras, representation theory and category theory.