This award funds the research activities of Professors Orlando Alvarez and Rafael Nepomechie at the University of Miami in Coral Gables, Florida.
The Standard Model that describes the known elementary particles is an example of a gauge theory. The still-unsolved problem of computing the hadron spectrum (the masses of protons, etc.) is an example of a strong-coupling problem in gauge theory. The discovery that certain gauge theories are equivalent to corresponding string theories, i.e., the so-called AdS/CFT correspondence, has revolutionized theoretical physics, since it offers a way to address such difficult strong-coupling problems. An important development has been the discovery and exploitation of integrability in AdS/CFT, which could lead to exact solutions of these theories. Professor Nepomechie's main objective is to apply techniques of integrable quantum spin chains and integrable quantum field theories to problems in gauge/string theory. In parallel, one of the big challenges in theoretical physics is why the gravitational force is very weak relative to the other basic forces. Professor Alvarez will therefore study a class of field theoretic models where there is no gravity in spacetime. These theories do not have a fundamental graviton, the quantum responsible for the gravitational force. What is interesting about these theories is that on lower-dimensional surfaces (the so-called branes) sitting inside the spacetime there is an induced weak theory of gravity. The gravitons only exist on the low-dimensional surface as an excitation of the geometry of the surface.
This project is also envisioned to have significant broader impacts. This work may open new directions in string theory and mathematics. Both Professors Alvarez and Nepomechie will provide scientific training to the next generation of scientists in Miami and also in Africa at the African Institute for Mathematical Sciences (AIMS) in Cape Town, South Africa. Their research findings will be disseminated through the internet and scientific publications, as well as through seminars and international conferences. The PI's will also give public lectures on their research at local schools and community centers.
