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
Representation theory of diagram algebras and logarithmic conformal field theory. Generalized models of polymers and percolation are notoriously difficult to handle mathematically, but can be described and solved using diagram algebras and logarithmic conformal field theory. Potential applications include polymer-like materials, filtering of drinking water, spatial spread of epidemics and bushfires, and tertiary recovery of oil.
Universal structures in stringy extra dimensions. The project aims to study properties of extra dimensions in string theory by means of techniques from supersymmetric gauge theory. This new approach makes it possible to study areas in the landscape of stringy extra dimensions that have not been accessible before. The project expects to uncover new universal features. This will have significant impact on string theory and mathematics. Expected outcomes of this project include answers to conceptua ....Universal structures in stringy extra dimensions. The project aims to study properties of extra dimensions in string theory by means of techniques from supersymmetric gauge theory. This new approach makes it possible to study areas in the landscape of stringy extra dimensions that have not been accessible before. The project expects to uncover new universal features. This will have significant impact on string theory and mathematics. Expected outcomes of this project include answers to conceptual questions in string theory, new types of extra dimensions, and new methods to compute quantum corrections in string theory. This should provide significant benefits, such as interdisciplinary collaborations at the national and international level and a strengthening of string theory in Australia.Read moreRead less
Logarithmic conformal field theory and the 4D/2D correspondence. Conformal field theory provides powerful methods for attacking problems in theoretical physics and furnishes beautiful connections between seemingly disparate branches of pure mathematics. This proposal aims to greatly expand our knowledge of the logarithmic conformal field theories that have recently witnessed a resurgence of interest in physics. Advancing these theories is crucial to progress in high-energy physics and pure mathe ....Logarithmic conformal field theory and the 4D/2D correspondence. Conformal field theory provides powerful methods for attacking problems in theoretical physics and furnishes beautiful connections between seemingly disparate branches of pure mathematics. This proposal aims to greatly expand our knowledge of the logarithmic conformal field theories that have recently witnessed a resurgence of interest in physics. Advancing these theories is crucial to progress in high-energy physics and pure mathematics. Expected outcomes include a completely new understanding of the mathematical structure of these theories which will, in turn, facilitate applications in 4D gauge theory. This will boost research capacity and further cement Australia's reputation as an international leader in mathematical physics 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
Special Research Initiatives - Grant ID: SR0354741
Funder
Australian Research Council
Funding Amount
$10,000.00
Summary
Quantum Many-Body Systems Network: Breakthrough Science and Frontier Technologies. This Initiative will bring together leading researchers with complementary expertise in mathematics and the enabling sciences to form a Network fostering world leading fundamental research and innovation in quantum many-body systems. The collaborative effort between mathematicians with powerful and sophisticated new techniques and physicists and chemists with deep insight into the challenges and opportunities of t ....Quantum Many-Body Systems Network: Breakthrough Science and Frontier Technologies. This Initiative will bring together leading researchers with complementary expertise in mathematics and the enabling sciences to form a Network fostering world leading fundamental research and innovation in quantum many-body systems. The collaborative effort between mathematicians with powerful and sophisticated new techniques and physicists and chemists with deep insight into the challenges and opportunities of the quantum realm will lead to breakthrough science of vital importance to the development of frontier technologies in Australia. This Network will also place a strong emphasis on research training, the mentoring of early career researchers and establishing collaborations with leading international research groups and networks.
Read moreRead less
Decoherence in quantum computing and quantum electromechanical systems. Australia is one of the world leaders in fundamental studies and implementation of quantum computing and quantum electromechanical systems. By developing a framework to quantify and control noise due to decoherence in such systems, this research will facilitate progress in the development and understanding of quantum computing and quantum electromechanical devices. The project will also significantly strengthen the general r ....Decoherence in quantum computing and quantum electromechanical systems. Australia is one of the world leaders in fundamental studies and implementation of quantum computing and quantum electromechanical systems. By developing a framework to quantify and control noise due to decoherence in such systems, this research will facilitate progress in the development and understanding of quantum computing and quantum electromechanical devices. The project will also significantly strengthen the general representation of research on decoherence, a field of crucial importance to many areas of theoretical and experimental physics, in Australia. Funding of this project will enable Australia to further expand its leading position in cutting-edge science and next-generation technology.
Read moreRead less
Discrete integrable systems. Discrete integrable systems are a fundamental generalisation of traditional integrable systems. This project, combining 5 world experts from 3 countries and 2 early career researchers, will expand and systematise this new interdisciplinary field, and will place Australia at the forefront of this intensive international activity.
Centre for Quantum Computer Technology. Development of a quantum computer (QC) for massively parallel computing is one of the major challenges in science and engineering this century. Since 2000 the Centre has achieved two major breakthroughs in this field: constructing the key functional element of a silicon solid-state QC; and co-inventing a scheme for efficient linear optics QC. The proposed CoE aims to align these two nationally co-ordinated research programs with the world's existing comput ....Centre for Quantum Computer Technology. Development of a quantum computer (QC) for massively parallel computing is one of the major challenges in science and engineering this century. Since 2000 the Centre has achieved two major breakthroughs in this field: constructing the key functional element of a silicon solid-state QC; and co-inventing a scheme for efficient linear optics QC. The proposed CoE aims to align these two nationally co-ordinated research programs with the world's existing computer and IT industries to realise a fault-tolerant multiple qubit quantum processor with integrated control and qubit chips, and develop a scaleable optical quantum processor providing significant economic benefit to Australia.Read moreRead less