Integrable Deformations in Holography

The goal of the overall project is to define and study the landscape of integrability preserving deformations of the AdS/CFT correspondence, and provide in-depth tests matching both sides of the correspondence through the development and application of exact integrability techniques. The AdS/CFT correspondence is a conjectured equivalence between string theories on anti-de Sitter spaces and conformal gauge theories, and has led to deep insights into both string and gauge theory, at the heart of modern theoretical particle physics. On the string theory side this project involves studying the quantum integrable structure of deformations with varying algebraic structures, not all compatible with standard approaches in the undeformed setting. On the gauge theory side this project involves the development of new noncommutative gauge theories, and the study of their observables via integrable spin chains. This project would extend and apply the power of integrability in AdS/CFT to a physically rich setting beyond supersymmetric and conformal gauge theories, with novel underlying algebraic structures.