Gabriele Tartaglino Mazzucchelli

Supersymmetric field theories on curved backgrounds and applications

During the last four decades, supersymmetry has been at the forefront of theoretical and mathematical physics of fundamental interactions. It played a crucial role in constructing models aimed at the unification of all forces including quantum gravity, namely string theory. Supersymmetry has also led to several new developments in mathematical physics such as, for example, the study of conformal field theories (that play a fundamental role in string theory and in the description of phase transitions in statistical mechanics) and integrable systems.

The analysis of supersymmetric theories on curved backgrounds has made possible the exact computation of several important observables. For instance, quantum computations in (super)conformal field theories on a conformally flat background, can be extrapolated from the curved to the flat space limit. For rigid supersymmetric field theories on curved spacetimes localisation techniques (which can reduce an infinite dimensional path integral to a fine dimensional one) allow one to compute quantum observables, such as the partition function, indices, correlators or Wilson loops exactly. Remarkably, localisation has been developed also for calculations in supergravity theories and evaluation of the quantum entropy of black holes. One crucial requirement of localisation is that SUSY has to close off-shell. This leads to the natural use of covariant off-shell (superspace) techniques.

In quantum field theories, correlation functions may contain singularities at coincident points, the so-called contact terms. They arise as higher-derivative terms in quantum effective actions on some supersymmetric gravity and gauge multiplet backgrounds. For correlation functions of symmetry currents, contact terms can lead to so-called anomalies. These manifest the breakdown of a symmetry due to short distance quantum effects. Anomalies have had a predominant role in the non-perturbative study of quantum field theory and string theory and relate to the Atiyah-Singer index theory in mathematics. In supersymmetric theories, anomalies lie in supermultiplets. Despite their importance, for general supersymmetry and spacetimes, the structure of higher-derivative invariants associated to contact terms and anomalies is not understood. These find important applications in the study supersymmetric quantum field theories, holographic correspondences between gauge and quantum gravity and related topics.

This project aims at: i) classifying general off-shell supersymmetric curved backgrounds by mean of new mathematical techniques; ii) studying supersymmetric and superconformal field theories on curved manifolds and their applications to holographic correspondences; iii) classify the structure of supersymmetric anomalies in generality.

This project will support the research of the ARC Future Fellowship of Dr. Gabriele Tartaglino Mazzucchelli “Supersymmetry and Supergravity: New Approaches and Applications.” The student will largely benefit from a vibrant international collaboration on supersymmetry and related topics.

Supersymmetry, Supergravity and String inspired models of Cosmology

During the last four decades, supersymmetry has been at the forefront of research in theoretical and mathematical physics of fundamental interactions. It played a crucial role in constructing models aimed at the unification of all forces including quantum gravity, namely string theory. As such, an active area of research is attempting to reconcile string theory with observed cosmology. Supersymmetry has also led to several new developments in mathematical physics.

Supergravity arises as the low-energy limit of string theory. Higher-order deformations of gravity give alternative descriptions of dark energy or dark matter and have recently become prominent in inflationary models; see for example the Starobinsky model. It has been recently shown that various higher-derivative supergravities lead to spontaneously broken supersymmetry and a dynamically generated positive cosmological constant. On one hand, this raised a renewed interest in extended supergravity models possessing de-Sitter (expanding universe) solutions in various dimensions. On the other hand, it remains an open question, and a subject of active debate in the string theory community, to understand whether these models are only effective theories or can be embedded in a consistent theory of quantum gravity.

Another breakthrough of the last two decades in research in string theory has been the discovery of holographic correspondences. These are theoretical tools connecting (D+1)-dimensional theories of (quantum) gravity to D-dimensional Quantum Field Theories (QFTs). The term holography is used in analogy to 2D holograms that can encode information about 3D objects. The best-established holographic conjectures involve supersymmetric theories. Several attempts to describe cosmological models by using holography have also been made.

This project aims at tackling open questions of string inspired cosmological models. A mathematical characterization of supergravity theories with spontaneously broken supersymmetry will be completed as a step towards understanding whether a positive cosmological constant and de-Sitter solutions can be consistent in string theory or different cosmological scenarios need to be found. Moreover, the project will explore also more exotic, but potentially revolutionary, holographic approaches to quantum cosmology.

Solvable supersymmetric field theories, string theory and AdS/CFT

During the last four decades, supersymmetry has been at the forefront of theoretical and mathematical physics of fundamental interactions. It played a crucial role in constructing models aimed at the unification of all forces including quantum gravity, namely string theory. Supersymmetry has also led to several new developments in mathematical physics such as, for example, the study of conformal field theories (that play a fundamental role in string theory and in the description of phase transitions in statistical mechanics) and integrable systems.

Supersymmetric quantum field theories in different space-time dimensions have been a fruitful ground of research to construct solvable models that shed new light on the dynamics of strongly coupled systems (such as the confinement of gauge theories), and our mathematical understanding of the physics of fundamental interactions. Some of the most impressive examples appeared in the last two decades in the context of the holographic AdS/CFT correspondences where integrability techniques, originally developed in statistical mechanics, started to play a crucial role in solving string theory models of quantum gravity. Holographic correspondences are theoretical tools connecting (D+1)-dimensional theories of (quantum) gravity to D-dimensional Quantum Field Theories (QFTs). The term holography is used in analogy to 2D holograms that can encode information about 3D objects. The best established holographic conjectures involve supersymmetric theories.

This project aims at expanding our knowledge of solvable/integrable quantum field and string theories by exploiting the technical advantages existing in supersymmetric theories and their deformations.

We will investigate deformations of integrable QFTs as a means of constructing new solvable models. Part of the project will look at a particular class of deformations, the so-called TTbar deformations, introduced by Zamolodchikov in 2004 for 2D QFTs. These deformations have received much attention in the high-energy theoretical physics community in the last few of years due to their application to the study of the AdS/CFT correspondence and for their impact in the field of 2D integrable QFTs. Extended also to dimensions higher than two, these deformations are starting to give new perspectives in understanding higher-derivative effective theories that arise in string theory and holographic correspondences where the energy spectrum can be solved exactly. Their extension to the supersymmetric case has been developed by Dr Tartaglino-Mazzucchelli, the Principal Advisor for this project, and his collaborators in a series of papers in 2018-2019. We plan to extend these results and develop a systematic understanding of supersymmetric TTbar deformations and their application to the AdS/CFT correspondence. We will then apply our findings to answer questions in these fields, including the detailed analysis of the spectrum and correlation functions of models on both sides of these correspondences.

This cutting-edge interdisciplinary research project will connect the very strong Australian mathematical physics community working on integrable systems with the research in theoretical physics that has characterized an international effort to construct a consistent unified theory of all fundamental interactions. This novel research synergy will enhance UQ’ and Australia’s position in mathematical and theoretical physics.

Supersymmetry and Supergravity: new approaches and applications

During the last four decades, supersymmetry has been at the forefront of theoretical and mathematical physics of fundamental interactions. It played a crucial role in constructing models aimed at the unification of all forces including quantum gravity, namely string theory. Supergravity arises as the low-energy limit of string theory and extends Einstein's General Relativity to an unifying framework of particles and forces.

This project aims at improving our understanding of general supersymmetric theories and supergravity-matter couplings. The outcomes of this project will advance our knowledge of supersymmetry and its mathematical formulation towards the solution of challenging open questions in the study of quantum field theories and gravity. The project’s results will find potential applications to various research branches of high-energy theoretical physics such as quantum field and string theories, matter-coupled gravity, cosmology and holographic dualities.