Theory of Elementary Particles

University Of Miami, Coral Gables FL

Investigators

Abstract

One of the most important recent developments in string theory is the discovery of integrability on both sides of the AdS/CFT correspondence. Nepomechie's main objective is to apply techniques of integrable quantum spin chains and integrable quantum field theories, which he has helped develop during the past two decades, to problems in string/gauge theory. He has already contributed to the understanding of exact bulk and boundary scattering matrices, which he plans to exploit to obtain further exact results. Alvarez will conduct research in quantum field theory and string theory. Alvarez is studying the extension of the elliptic genus to families of Dirac-Ramond operators. The families index theorem of Atiyah and Singer for the Dirac operator can be used in gauge theories to study the anomalies that spoil the quantization of the theory. The analog in string theory should be a families index theorem for the Dirac-Ramond operator. Even though we do not really know what is string theory, this families index theorem should give us some information about the structure of the theory beyond perturbation theory. This is an important attempt at trying to learn about non-perturbative aspects of string theory. The broader impacts of this research are as follows: this work may open new directions in string theory, mathematics, as well as condensed matter physics and statistical mechanics. Both Alvarez and Nepomechie will help provide scientific training to the next generation of American citizens, in particular to those from the Latino community in Miami. Their findings will be disseminated through the internet and scientific publications, as well as through seminars and international conferences. The PIs also give lectures at local public schools on science.