Andrzej Jarosz

Title: Beyond Planar and Thermodynamic Limits in the Context of Spinning Strings in the AdS/CFT Correspondence

A thesis submitted for the degree of Doctor of Philosophy on March 3rd, 2009.

The Niels Bohr Institute
The Graduate School
of Science
Faculty of Science
University of Copenhagen
Denmark

Supervisor:
Charlotte Kristjansen

Abstract

Beyond Planar and Thermodynamic Limits in the Context of Spinning Strings in the AdS/CFT Correspondence

The thesis starts with a general introduction to the AdS/CFT correspondence and subsequently describes two research projects related to this correspondence. The first project aims at obtaining the two-loop correction to the energy of a certain spinning string by means of the so-called quantum string Bethe ansatz. The result of the computation on one hand constitutes a prediction for string theory and on the other hand makes possible a test of a conjectured phase factor playing a central role in the derivation of the Bethe ansatz.

The second research project addresses non-planar corrections to the conformal dimension of a set of field theory operators which are dual to folded, rotating strings. The corrections are known to be the eigenvalues of a certain operator, the non-planar dilatation operator, and it is suggested that the matrix elements of this operator can be computed using a coherent state formalism. Based on the scaling of these matrix elements, calculated as suggested, a prediction for the scaling of the genus one correction to the string energy is given.