Investigation of k-string energy using the gauge/gravity correspondence

The AdS/CFT correspondence, or in a more general sense, the gauge/gravity correspondence, is a duality between a string theory or gravity defined on one space and a gauge theory living on the conformal boundary of the same space. The AdS/CFT correspondence has drawn a tremendous amount of attention since the late 1990's. After all, it sounds so promising and exciting to connect two drastically different looking theories, gravity and gauge theory, directly.

A lot of effort has been put into the gauge/gravity correspondence related research from the physics community, hoping that connections between string theories and corresponding gauge theories with less supersymmetry would be discovered and more observables of the gauge theory could be calculated in terms of string theory and supergravity. The k-string tension calculation using the gauge/gravity correspondence has been one of many such attempts.

k-string tension is a crucial topic in quark confinement and strong interactions. In this dissertation, we investigate k-strings in d = 3 and d = 4 spacetime dimensions using the gauge/gravity correspondence. Exploiting the similarities between two supergravity backgrounds, i.e., the Maldacena-Nunez background and the Maldacena-Nastase background, we carry out calculations for k-string energies in d = 3 and d = 4 spacetime dimensions. The specific calculations investigated are the lowest order tension term for the energy of k-strings and the first order, one loop corrections, i.e., the Lüscher term. The tension term is proportional to L, the length of quark-antiquark pairs and the Lüscher term is the typical 1/L Coulombic correction. We reproduced the sine law for the tension term and the Lüscher term which agree with the results from lattice gauge theory.

We also briefly compare the resluts of the Klebanov-Strassler background with the Maldacena Nunez and the Maldacena Nastase backgrounds, with the hope to summarize and generalize the k-string energy calculations in the context of gauge/gravity correspondence using different supergravity backgrounds that have similar geometry.