Physics Department Senior Design Project Proposal

Project Mentor: Alex Flournoy, 303-273-3712, [email protected] (Name, phone, email) Project Title: The AdS/CFT correspondence – A Tool from String Theory

Project Type: [ ] Team; Number of students__1___ [ X] Honors Objective (What is the science and/or engineering in this project?)

The AdS/CFT correspondence is perhaps one of the most useful results to arise from String Theory since its discovery. Questions about the role of String Theory as a “fundamental theory” aside, this particular result, relating calculations in non-gravitational field theory to purely gravitational calculations, promises to bridge the fields of high-energy/gravitational and condensed-matter physics in an unprecedented manner. It is the opinion of many in the field that this result serves as the basis for the future of research in String Theory as a “tool” for computation. A student who can grasp even the basic notions behind this correspondence will be in an advantageous position to enter particle/gravitational/condensed-matter studies/research with a unique and powerful perspective.

Of course a proper understanding of this result requires an extensive background in advanced general relativity, particle physics, string theory and the mathematics of conformal field theory. This can render the correspondence a prohibitive tool to consider for even for expert theorists if they do not have a broad enough background. A clean presentation of the correspondence that would be suitable for implementation by theorists without the full background is lacking. Constructing such a presentation and a “manual” for the use of the tool is the chief goal of this senior design project.

In terms of design, the student will have to choose the essential ideas that are needed to utilize the correspondence as a calculational tool. The “client” for the task would be the community of theorists who use field theory including nuclear theorists, condensed matter and particle theorists.

Prior Background (What is the history of your involvement with this topic, including previous student projects?)

The Ads/CFT correspondence has been the subject of ever increasing research in String Theory. The result was born as the culmination of many of the developments over the last ten years in the field. My own research on D- branes, extra-dimensions, conformal field theories, and supergravities has given me the expertise on how this result arises within the framework of String Theory.

Student Expectations (What are the deliverables (in addition to the lab notebook and reports) for the two-semester project?)

The student will create a clear and concise “manual” for implementation of the correspondence with a few examples carefully chosen and worked out by the student. The student will make a present the results in both the Theory Seminar, and in the Particle Physics course..

Supervision Plan (Who will be directly interacting with the student(s), you, a post-doc, grad students, or others?)

I will be interacting with the student.

Resources (What equipment, algorithms, and facilities are available, and what will be assembled as part of the project?)

The student will assemble a manual for using the Ads/CFT tool, including a translation dictionary for calculations done on each side of the correspondence. Physics Department Senior Design Project Proposal

Technical References (Identify a few key starting points for the student(s); journal citations, prior reports, instruction manuals, etc.)

The Large N limit of superconformal field theories and supergravity. Juan Martin Maldacena, (Harvard U.) . HUTP-98-A097, Nov 1997. 19pp. Published in Adv.Theor.Math.Phys.2:231-252,1998, Int.J.Theor.Phys.38:1113-1133,1999

Anti-de Sitter space and holography. Edward Witten, (Princeton, Inst. Advanced Study) . IASSNS-HEP-98-15, Feb 1998. 39pp. Published in Adv.Theor.Math.Phys.2:253-291,1998.

TASI 2003 Lectures on AdS/CFT Authors: Juan M. Maldacena