Nonperturbative Quantum Fields and Strings

点击翻译按钮获取中文摘要

Quantum Field Theory (QFT) exemplifies the power of principles in physics. It is the inevitable framework merging two of the most fundamental and transformative principles in science: Quantum Mechanics and Relativity. Because of this, QFT is at the heart of all modern physics. It describes, with unprecedented success, many phenomena in nature, including in high energy physics, cosmology and condensed matter physics.**The predictions of QFT describing the Standard Model of Particle Physics have been spectacularly confirmed by the discovery of the Higgs boson at the Large Hadron Collider. Further, recent data from the Planck satellite have strengthened the picture explaining the origin of the large scale structure of the Universe as being seeded by fluctuations of a quantum field. These are unparalleled triumphs in the history of QFT. Despite these, our understanding of QFT in the strong coupling regime, where textbook perturbative techniques breakdown, is very far from complete.**My research program will investigate the physical properties that systems that are strongly coupled can exhibit. The strategy is to use tools that I have helped develop to study QFTs exhibiting rich phenomena with enough symmetry to allow an exhaustive understanding of the dynamics even in the strong coupling regime. The objective is to obtain formulas that are exact functions of the coupling constant of the theory, thus giving physicists a precious window into nonperturbative physics.***A related theoretical and experimental challenge is to characterize all the possible states/phases of matter that can be formed in tabletop experiments, in the early universe and in particle accelerators, specially in strongly coupled systems. We aim to identify and compute new observables in QFTs and lattice Hamiltonians, known as order parameters, that distinguish the different phases that a quantum system may support. Identifying new observables that distinguish the different phases is an important theoretical tool for predicting hitherto unknown states of matter in Nature.**The Holographic Principle has resulted in a transformation of our understanding of string and M- theory, which is our most promising approach towards a unified quantum theory of the universe, thanks to the so-called AdS/QFT correspondence. This correspondence identifies a non-gravitational QFT with string/M-theory in Anti-de-Sitter space (AdS). However, our inability to understand string theory in AdS beyond the point particle approximation, invalidates the use of the AdS/QFT correspondence to compute strongly coupled phenomena in confining gauge theories like Quantum Chromodynamics. This requires taming the physics of string theory in curved geometries in the strong coupling regime.**We propose to perform the first exact computations of string theory in AdS. These will capture all corrections to the point particle approximation to string theory. We will study string amplitudes with suitable boundary conditions that allow an exact evaluation of the Feynman's path integral on the string worldsheet theory by localization of the functional integral. The time is ripe to tackle this problem. The insights obtained in the computation of these special amplitudes will provide new vistas on what string theory is in curved spacetimes.**Understanding physics in the nonperturbative regime can find many applications, giving us a new framework to manipulate strongly interacting systems, which may result in new technologies and materials, and an environment on which to build a Quantum Computer. The discovery of operators characterizing new phases, in turn, can motivate experiments to produce these new new quantum states of matter, with unforeseen technological spinoffs.