Exploring Structure and Symmetry in String Theory and Field Theory

点击翻译按钮获取中文摘要

This award funds the research activities of Professor Savdeep Sethi at the University of Chicago. The origins of space and time are among the enduring mysteries of nature. Did space and time emerge in some kind of Big Bang? Will the universe end in a Big Crunch? Is there really a multiverse of possibilities? In order to answer such basic questions about the nature of space and time, we need a quantum theory of gravity. String theory is our best candidate for such a theory. In his research, Professor Sethi aims to explore structure and symmetry in both string theory and the kinds of so-called "quantum field theories" of interest to particle physicists and condensed-matter physicists. This research program is therefore in the national interest by advancing the development of the infrastructure of basic science in the United States. This research program also has concomitant broader impacts in three areas. The first comes from providing research opportunities for undergraduates, including continued participation in the Summer REU Opportunities for Minorities and Women program at the University of Chicago. The second is through continued participation in both the Space Explorers inner-city K-12 enrichment program and the Life-Long Learning (L3) program. The final aspect involves improved interdisciplinary ties with both cosmologists and mathematicians through lectures at schools and workshops, through direct collaboration, and through the organization of relevant scientific meetings.More technically, the goals of Professor Sethi's research center around two broad themes. The "structure" aspect of this research involves exploring landscapes in field theory and string theory. This will involve a number of topics, among them the description of flux backgrounds from a field-theory perspective and their realization in string theory via a novel landscape of anti-de Sitter space solutions; the development of flux vacua in M-theory and type IIA string theory; the role of anti-branes in flux vacua; the exploration of constraints on inflating and de Sitter constructions in string theory; the construction of accelerating space-times using stringy domain-wall solutions; and the study of chiral gauge theory in two dimensions and its relation to new geometric structures. By contrast, the "symmetry" aspect of the proposal involves exploring the implications of spontaneously broken symmetries in gravity and in effective field theory. The questions in gravity revolve around the extent to which the dynamics of gravitational lumps is determined by symmetry. In a broader context, anomalous and non-anomalous global symmetries can constrain effective field theory couplings with implications for condensed-matter systems such as quantum Hall systems. The final set of questions involve supersymmetry in two ways: first to develop a symbolic computation package that can generate supersymmetric Lagrangians with higher-derivative couplings (a long-needed tool that will have a host of applications in both string theory and field theory), and second to explore surprising simplifications in the vacuum structure of supersymmetric quantum-mechanics models.