Superstring holography and integrability in AdS_5 x S^5
Ian Swanson
TL;DR
This work investigates the AdS/CFT correspondence beyond the BMN limit by combining a virial expansion of N=4 SYM operator dimensions with a curvature expansion of strings on AdS5×S5. It develops a systematic framework to compute and compare string energies and gauge-theory anomalous dimensions across multiple impurity sectors (su(2), sl(2), su(1|1)) and up to three-loop order, revealing precise agreement up to two loops and a persistent mismatch at three loops. The thesis further demonstrates that a curvature-corrected Green-Schwarz string in the pp-wave background organizes into extended supermultiplets in line with PSU(2,2|4) symmetry, and that an all-orders-in-λ′ Bethe-like structure emerges for the su(2) sector near the pp-wave limit. Overall, the results provide strong evidence for integrable structures in both theories at lower orders while highlighting subtle breakdowns at higher loops, motivating ongoing refinements in the holographic dictionary and gauge/string integrability programs.
Abstract
The AdS/CFT correspondence provides a rich testing ground for many important topics in theoretical physics. The earliest and most striking example of the correspondence is the conjectured duality between the energy spectrum of type IIB superstring theory on AdS_5 x S^5 and the operator anomalous dimensions of N=4 supersymmetric Yang-Mills theory in four dimensions. While there is a substantial amount of evidence in support of this conjecture, direct tests have been elusive. The difficulty of quantizing superstring theory in a curved Ramond-Ramond background is compounded by the problem of computing anomalous dimensions for non-BPS operators in the strongly coupled regime of the gauge theory. The former problem can be circumvented to some extent by taking a Penrose limit of AdS_5 x S^5, reducing the background to that of a pp-wave (where the string theory is soluble). A corresponding limit of the gauge theory was discovered by Berenstein, Maldacena and Nastase, who obtained successful agreement between a class of operator dimensions in this limit and corresponding string energies in the Penrose limit. In this dissertation we present a body of work based largely on the introduction of worldsheet interaction corrections to the free pp-wave string theory by lifting the Penrose limit of AdS_5 x S^5. This provides a new class of rigorous tests of AdS/CFT that probe a truly quantum realm of the string theory. By studying the correspondence in greater detail, we stand to learn not only about how the duality is realized on a more microscopic level, but how Yang-Mills theories behave at strong coupling. The methods presented here will hopefully contribute to the realization of these important goals.