The fundamental laws of nature, to the best of our knowledge, are described by the Standard Model of particle physics, which is based on Quantum Field Theory (QFT). QFTs are quantum mechanical systems with an infinite number of degrees of freedom. The quantum systems are in general incredibly complicated to study. Even for one degree of freedom we face a second order differential equation, which can be solved analytically in only a few cases. For a system of a few particles one needs supercomputers to solve the Schrödinger equations approximately. Therefore, dealing with infinitely many degrees of freedom in QFT is a problem of extreme complexity. The aim of this project is to find the complete solution of a fully interacting 4D QFT for the first time using integrability.
For more than 70 years a lot of effort was spent trying to efficiently get physical predictions from QFTs. Nevertheless, we still have a rather fragmented and often only qualitative knowledge of the physical picture. This is because most analytical calculation methods in QFTs are largely based on the weak coupling perturbation expansion or through Monte-Carlo simulations, which require costly computer simulations with rather limited precision.
Recently a new set of ideas based on integrability and holography were introduced.
Integrability was first introduced for mechanical systems, where the existence of extra integrals of motion frequently allowed one to get solutions in a closed form. When our QFT is integrable one can hope to be able to access physical results completely non-perturbatively at finite values of the system’s parameters. This is extremely complex and requires case-by-case investigation, but is worth it due to the potential to find incredibly powerful results. Until recently, all known integrable techniques applicable to QFTs were limited to 2D. Using holography one can then map a more realistic 4D QFT (3 space + 1 time) to a 2D world sheet and thus apply the integrability methods to access new physical phenomena.
The PI was responsible for several breakthroughs in the field of integrability and holography. In one of them, the PI managed to solve a major problem: finding the spectrum – or equivalently the two-point correlation functions – of these theories. With his collaborators, he pioneered a ground-breaking discovery: they found exact equations for the spectrum of simple but highly non-trivial excited string states (published and highlighted by editors in Phys. Rev. Lett.). This powerful set of equations became known as the Quantum Spectral Curve (QSC).
The project is dedicated to pushing those exciting developments to the next level – by combining the QSC with the powerful method of Separation of Variables, which we believe will allow us to gain access to all physically relevant quantities in this class of QFTs. In turn, this would constitute the solution of a 4D QFT for the first time – which is the aim of this project.
