Integrable Systems in Gauge and String Theories. Gauge theory describes all quantum forces except gravity. String theory aims to describe quantum gravity. Both theories are widely believed to be different limits of one unknown theory. Discoveries of integrable nonlinear partial differential equations and integrable quantum systems in gauge/string theories are among the most remarkable recent developments in mathematical physics. They have led to deep results in known gauge/string theories, as we ....Integrable Systems in Gauge and String Theories. Gauge theory describes all quantum forces except gravity. String theory aims to describe quantum gravity. Both theories are widely believed to be different limits of one unknown theory. Discoveries of integrable nonlinear partial differential equations and integrable quantum systems in gauge/string theories are among the most remarkable recent developments in mathematical physics. They have led to deep results in known gauge/string theories, as well as to viable paths towards the unknown theory that interpolates them. This project contributes to these developments by adapting and developing sophisticated technical tools and insights from integrable models to shed light on that unknown theory that transcends the gauge/string gap. Read moreRead less
Integrable models and topological strings. This project aims to develop advanced methods to compute n-point correlation functions in two-dimensional integrable models. The project expects to use recently discovered connections with topological strings to compute currently-inaccessible conformal blocks in conformal field theories, and their analogues in integrable massive field theories and statistical mechanical models. Expected outcomes include explicit expressions for the n-point correlation ....Integrable models and topological strings. This project aims to develop advanced methods to compute n-point correlation functions in two-dimensional integrable models. The project expects to use recently discovered connections with topological strings to compute currently-inaccessible conformal blocks in conformal field theories, and their analogues in integrable massive field theories and statistical mechanical models. Expected outcomes include explicit expressions for the n-point correlation functions, advances in the theory of topological vertices and the related representation theory, and new solutions of the Yang-Baxter equations. This should provide benefits that include a better understanding of two-dimensional integrable models and their deep connections with topological strings.Read moreRead less
New approaches and applications of integrable quantum field theory. This project aims to develop new mathematical approaches to the theory of integrable systems to obtain exact solutions of various non-linear models of two-dimensional quantum field theory. The project is based on an unexpected correspondence between classical and quantum systems which provides a powerful method for describing physically interesting models of integrable quantum field theory. Expected outcomes include exact soluti ....New approaches and applications of integrable quantum field theory. This project aims to develop new mathematical approaches to the theory of integrable systems to obtain exact solutions of various non-linear models of two-dimensional quantum field theory. The project is based on an unexpected correspondence between classical and quantum systems which provides a powerful method for describing physically interesting models of integrable quantum field theory. Expected outcomes include exact solutions to non-linear sigma-models which have important applications in many areas, including condensed matter physics, string and field theories and Riemannian geometry. The project expects to provide significant benefit to the advancement of knowledge in physics and mathematics.Read moreRead less
Indecomposable representation theory. The project aims to develop a systematic approach to the study and application of indecomposable representations in pure mathematics and mathematical physics. Indecomposability is a central concept in representation theory and is thus fundamental to a wide range of applications in science. Examples of important contexts considered are diagram algebras and finite and infinite-dimensional Lie algebras including the Virasoro algebra underlying conformal field t ....Indecomposable representation theory. The project aims to develop a systematic approach to the study and application of indecomposable representations in pure mathematics and mathematical physics. Indecomposability is a central concept in representation theory and is thus fundamental to a wide range of applications in science. Examples of important contexts considered are diagram algebras and finite and infinite-dimensional Lie algebras including the Virasoro algebra underlying conformal field theory. Linear algebra is a ubiquitous mathematical tool playing a pivotal role in representation theory, and the project aims to resolve outstanding fundamental issues concerning families of so-called non-diagonalisable matrices.Read moreRead less
Mathematical models for disordered critical point theories. This project sets up a team to develop innovative techniques for fundamental advances in critical behaviour of disordered systems including the Nobel Prize winning integer quantum Hall effect. It will yield new mathematical models for disordered critical point theories, essential for the theoretical analysis of associated emerging technologies.
Advances in Conformal Field Theory with Extended Symmetry. This project aims to develop novel methods to formulate conformal field theories with extended symmetry that are important in variety of applications ranging from pure mathematics to phenomenology of elementary particles. The project expects to advance our knowledge in the most challenging areas of modern theoretical physics - Quantum Gravity and physics beyond the Standard Model of particle physics. Its expected outcomes will include co ....Advances in Conformal Field Theory with Extended Symmetry. This project aims to develop novel methods to formulate conformal field theories with extended symmetry that are important in variety of applications ranging from pure mathematics to phenomenology of elementary particles. The project expects to advance our knowledge in the most challenging areas of modern theoretical physics - Quantum Gravity and physics beyond the Standard Model of particle physics. Its expected outcomes will include conceptual results of major significance for modern theoretical and mathematical physics, thus placing Australia at the forefront of this research. A rich intellectual environment will be provided for training Australian PhD students by internationally recognised experts.
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Novel Conformal Techniques in Quantum Field Theory, Gravity and Supergravity. Conformal symmetry is the maximal spacetime symmetry in relativistic quantum theory. This project will explore the dynamics of those quantum field theories and matter-coupled gravity theories that possess conformal symmetry and have recently been the focus of enormous interest worldwide. Its scientific outcomes will include a deeper understanding of Wilson loops in Yang-Mills theories, scattering amplitudes in conforma ....Novel Conformal Techniques in Quantum Field Theory, Gravity and Supergravity. Conformal symmetry is the maximal spacetime symmetry in relativistic quantum theory. This project will explore the dynamics of those quantum field theories and matter-coupled gravity theories that possess conformal symmetry and have recently been the focus of enormous interest worldwide. Its scientific outcomes will include a deeper understanding of Wilson loops in Yang-Mills theories, scattering amplitudes in conformal gravity and supergravity as well as other conceptual results of major importance to modern mathematical physics, thus placing Australia at the forefront of this research. A rich intellectual environment will be provided for training of Australian PhD students by internationally recognised experts. Read moreRead less
Advances in HIgher Spin Gauge Theory. This project aims to explore the dynamical and geometrical aspects of higher spin gauge theory that have recently become the focus of enormous interest worldwide. Higher spin gauge theory is a unique generalisation of Einstein’s gravitation theory, which possesses maximal gauge symmetry and is a novel candidate for quantum gravity. Expected project outcomes include a better understanding of higher-spin interaction vertices, correlation functions, and other c ....Advances in HIgher Spin Gauge Theory. This project aims to explore the dynamical and geometrical aspects of higher spin gauge theory that have recently become the focus of enormous interest worldwide. Higher spin gauge theory is a unique generalisation of Einstein’s gravitation theory, which possesses maximal gauge symmetry and is a novel candidate for quantum gravity. Expected project outcomes include a better understanding of higher-spin interaction vertices, correlation functions, and other conceptual results of major importance to mathematical physics.Read moreRead less
Ubiquity of K-theory and T-duality. An abstract mathematical tool, called K-theory, has recently found application in two, not obviously related, areas of physics: the classification of D-branes in String Theory, and topological phases in Condensed Matter Theory. This project aims to advance the development of K-theory using ideas from physics. In particular, the project aims to generalise previous constructions, such as T-duality, to loop spaces, and to develop the K-theory relevant to the clas ....Ubiquity of K-theory and T-duality. An abstract mathematical tool, called K-theory, has recently found application in two, not obviously related, areas of physics: the classification of D-branes in String Theory, and topological phases in Condensed Matter Theory. This project aims to advance the development of K-theory using ideas from physics. In particular, the project aims to generalise previous constructions, such as T-duality, to loop spaces, and to develop the K-theory relevant to the classification of topological phases in strongly interacting systems. This project involves postgraduate training as a crucial tool in achieving its aims and enhances Australia's position at the forefront of international research.Read moreRead less
Towards higher rank logarithmic conformal field theories. This project aims to expand our knowledge of logarithmic theories. Conformal field theory provides powerful methods for attacking problems in theoretical physics and furnishes beautiful connections between seemingly disparate branches of pure mathematics. Advancing these theories is crucial to progress in statistical mechanics, string theory and various mathematical disciplines. Expected outcomes include a detailed formalism for systemati ....Towards higher rank logarithmic conformal field theories. This project aims to expand our knowledge of logarithmic theories. Conformal field theory provides powerful methods for attacking problems in theoretical physics and furnishes beautiful connections between seemingly disparate branches of pure mathematics. Advancing these theories is crucial to progress in statistical mechanics, string theory and various mathematical disciplines. Expected outcomes include a detailed formalism for systematically and rigorously analysing a wide variety of logarithmic conformal field theories so as to facilitate applications.Read moreRead less