Classical string solutions in the AdS/CFT correspondence

Andrew W Irrgang, Purdue University

Abstract

This dissertation studies the properties of fields generated by moving charged particles in a strongly interacting gauge theory. In classical electro-magnetism, calculating the fields produced by moving charges is straight forward, but in a strongly interacting non-abelian theory, such as QCD, this not the case due to large quantum effects and the theory being non-linear. Recently, the AdS/CFT correspondence made these calculations feasible, though still non-trivial. Interestingly from a physics point of view, the fields produced by the moving charges are represented by a string. Solving for the string's changing shape is possible due to a nice mathematical application of integrability techniques involving Riemann Theta functions. The first case of consideration is a quark and anti-quark rotating about their center of mass. Such a configuration is described by a rigidly rotating open string with endpoints in the boundary of AdS5. Various cases of angular motion of the quark/anti-quark pair in the boundary is analyzed using an associated 1-d integrable Neumann-Rosochatius system. A solution is found from which the energy and angular momenta of the configuration, ie, the field between the charged particles, is calculated after being properly regularized. The work continues by investigating open strings with endpoints in the boundary of AdS that follow more generic trajectories. Utilizing integrability techniques, the equations of motion are solved when the string moves in AdS3. The Pohlmeyer reduction reduces the equations of motion to a generalized Sinh-Gordon equation from which three cases are studied: the Liouville, Sinh-Gordon, and Cosh-Gordon equations. Solutions to the Sinh and Cosh-Gordon equations are written in terms of Riemann Theta functions and numerical examples of these solutions are presented.

Degree

Ph.D.

Advisors

Kruczenski, Purdue University.

Subject Area

Physics

COinS