## Mid-Term Report Summary - EXQFT (Exact Results in Quantum Field Theory)

Quantum Field theory (QFT) is a universal language for theoretical physics, describing the Standard Model, Gravity, Early Universe, and Condensed Matter phenomena such as Phase Transitions, Superconductors, and Quantum Hall Fluids.

A triumph of 20th century physics was to understand weakly coupled QFTs: theories whose interactions can be treated as small perturbations of otherwise freely moving particles. However, weakly coupled QFTs represent a tiny island in an ocean of possibilities. They cannot capture many of the most interesting and important physical phenomena, from the strong nuclear force to high temperature superconductivity.

The critical challenge for the 21st century is to understand and solve strongly coupled QFTs. Meeting this challenge requires new physical insight, new mathematics, and new computational tools.

We have tried to address the problem of strongly coupled quantum field theories through two complementary strategies. One strategy is to think about some general foundational properties of quantum field theories and the other strategy is to understand in detail toy examples.

One striking property of QFT is the emergence of a large symmetry group at very long and very short distances. We have made some progress on elucidating the origin of this symmetry group as well as analyzing the consequences of this symmetry group for various interesting observables.

We have also used these techniques to study disordered systems, demonstrating the utility of QFT across different disciplines of theoretical physics.

Supersymmetric theories have been long understood to be an interesting arena for studying strongly coupled quantum physics. Many questions which are usually out of reach can be adequately addressed in the context of supersymmetric theories. We have studied supersymmetric theories in curved space times, demonstrating that the partition functions of such theories depend only on relatively few parameters and explaining some of the results obtained in the literature within this general framework. We have also found a new interpretation of the four-sphere partition function in some supersymmetric theories. It turns out to compute the geometric distance between different quantum field theories, providing new invaluable information on some of the simplest strongly coupled supersymmetric theories.

A triumph of 20th century physics was to understand weakly coupled QFTs: theories whose interactions can be treated as small perturbations of otherwise freely moving particles. However, weakly coupled QFTs represent a tiny island in an ocean of possibilities. They cannot capture many of the most interesting and important physical phenomena, from the strong nuclear force to high temperature superconductivity.

The critical challenge for the 21st century is to understand and solve strongly coupled QFTs. Meeting this challenge requires new physical insight, new mathematics, and new computational tools.

We have tried to address the problem of strongly coupled quantum field theories through two complementary strategies. One strategy is to think about some general foundational properties of quantum field theories and the other strategy is to understand in detail toy examples.

One striking property of QFT is the emergence of a large symmetry group at very long and very short distances. We have made some progress on elucidating the origin of this symmetry group as well as analyzing the consequences of this symmetry group for various interesting observables.

We have also used these techniques to study disordered systems, demonstrating the utility of QFT across different disciplines of theoretical physics.

Supersymmetric theories have been long understood to be an interesting arena for studying strongly coupled quantum physics. Many questions which are usually out of reach can be adequately addressed in the context of supersymmetric theories. We have studied supersymmetric theories in curved space times, demonstrating that the partition functions of such theories depend only on relatively few parameters and explaining some of the results obtained in the literature within this general framework. We have also found a new interpretation of the four-sphere partition function in some supersymmetric theories. It turns out to compute the geometric distance between different quantum field theories, providing new invaluable information on some of the simplest strongly coupled supersymmetric theories.

## Contact

**Record Number**: 189586 /

**Last updated on**: 2016-10-12