Analytic Studies of Strongly Coupled Systems

Strongly coupled systems comprise some of the most difficult and important problems in physics, from high temperature superconductivity, to quantum chromodynamics, to quantum gravity. Even the most basic questions about these systems such as the phase structure or the relevant degrees of freedom remain unanswered. It is necessary to develop new and imaginative techniques to understand the strongly dynamics of these systems.

Embedding of quantum field theories into string/M-theory, proposed to describe all physical phenomena in the Universe including quantum gravity in a single unified framework, has led to many new insights into strongly coupled dynamics. In particular, it provides a uniform and powerful picture of various quantum field theory phenomena and points to hidden relations between them. The gauge/gravity correspondence is one of prominent examples, which plays a key role in providing novel predictions for the strongly coupled behavior. However, fascinating details of the dynamics underlying these outcomes still remain unaccessible.

One can learn important features of the strongly couples systems by studying solvable models whose behaviors are well-controlled by nontrivial symmetries such as supersymmetry and integrability. Over the last few years, we have indeed made remarkable achievements in finding new quantities which are exactly computable no matter how strong the interactions are. They provide both quantitative and qualitative insight into known and new strongly coupled systems. For instance, these quantities have been used to confirm several detailed predictions of the gauge/gravity duality.

The very fruitfuil idea of supersymmetric localisation techniques, which reduce a path-integral of supersymmetric theories to an ordinary integral over a finite number of degrees of freedom, provides recent developments in studying strongly coupled systems. Many of early works with SUSY localisation techniques have been concerned with mathematical quantities, whose potential applications to physics are limited. It has been recently noticed that these techniques are very useful to compute more physical quantities of supersymmetric theories.

The goal of this project is to develop these new techniques to perform analytic studies of strongly coupled systems. In particular, I will study conformal theories in three and six dimensions that live on M2 and M5 branes in M-theory, respectively. It is extremely important to understand these theories as they will shed light on i) the very nature of mysterious M-theory and ii) the hierarchy of supersymmetric field theories. Moreover, three-dimensional conformal theories recently turn out to play a key role in quantum criticality in condensed matter systems. Another aim is to refine our knowledge of a set of specific states in supersymmetric theories, known as the BPS spectrum, which provides deep quantitative insights into the strong dynamics and the microscopic origin of black hole entropy.

The project therefore lies at the forefront of investigations and these results are expected to become important touchstones for the quantum field theory, string/M-theory, and even condensed matter communities. They will be also very likely to backreact on the pure mathematics.