Recent advances in understanding String Theory on boundaries have led to seeing connections between classical Gravity in 10 dimensions and Conformal Field Theories in 4 dimensions. This proposal will explore further the relation between string and gauge theories to understand the structure of hadrons. The main idea is to improve the understanding of the AdS/CFT correspondence, so that similar methods could be applied to the theory of strong interactions Quantum Chromodynamics (QCD). As stepping stones to the main goal are the PI intends to study field theory planar diagrams in light-cone gauge. He hopes to understand the emergence of strings from a field theory as a tool for describing long gauge invariant operators. He will look for new solutions to the string equations of motion with characteristic properties that make them identifiable in the field theory side of the correspondence. He will also look at generalizations of cusp anomaly calculations to better understand the dynamics of gluons in gauge theories with supersymmetries. The PI plans to give as part of his outreach a series of popular introductory lectures on string theory and particle physics at the QuarkNet Center at Purdue. He also intends to give lectures at the Tindley Accelerated School (98% minority student population).
One of the most important recent developments in theoretical physics was the so called AdS/CFT correspondence which establishes a relation between string theory and gauge theories. It lead lo new insights in the physics of space-time, black holes, quantum gravity and allowed the solution of difficult problems in a simple way. This project took advantage of those develompments and also help to better understand them. Results were obtained in three different directions of study. This new techniques were applied to the study of (supersonic) shock waves, in particular computing the thickness of the shock in terms of its velocity. We also found new properties of black holes, for example the fact that shock waves propagate on their horizons. Another topic was the study of the motion of strings in curved spaces which is necessary to better describe string theory in this context. Finally, a topic of interest in this duality is the study of surfaces of minimal area in hyperbolic spaces. Before our study only a few such surfaces were known but we found an infinite class of examples that can be used to improve our understading of the AdS/CFT correspondence. Moreover, surfaces of minimal area are important in many other contexts such as mathematics or even the study of cell membranes. Finally those results were the topic of several talks we delivered in local high schools. This will help advance the interest of the community in this type of research and help prepare a new generation of phsyicists. The results also lead to one Ph.D. dissertation and will also be part of two other Ph. D. dissertations in the near future.
